MATH221_Week_5_Homework

1.

Student: Jorge Ithier

Date: 12/1/16

Instructor: Alexandra Wrigley Course: Statistics for Decision Making

(100)

Assignment: Week 5 Homework 40 pts

1: Standard Normal Distribution Table (Page 1)

Find the area of the shaded region. The graph depicts the standard normal distribution

with mean 0 and standard deviation 1.

Click to view page 1 of the table. Click to view page 2 of the table.1 2

The area of the shaded region is ..7019

(Round to four decimal places as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

1 of 15 12/1/2016 11:20 PM

2: Standard Normal Distribution Table (Page 2)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

2 of 15 12/1/2016 11:20 PM

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

3 of 15 12/1/2016 11:20 PM

2.

3: Area under the standard normal distribution to the left of Z (page 1)

4: Area under the standard normal distribution to the left of Z (page 2)

Find the area of the indicated region under the standard normal curve.

Click here to view page 1 of the standard normal table.3

Click here to view page 2 of the standard normal table.4

The area between z and z under the standard normal curve is .= 0 = 1.2 .3849

(Round to four decimal places as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

4 of 15 12/1/2016 11:20 PM

3.

4.

Assume the random variable x is normally distributed with mean and standard deviation . Find the indicated

probability.

= 82 = 4

P(x )< 78

P(x ) (Round to four decimal places as needed.)< 78 =

Assume the random variable x is normally distributed with mean and standard deviation . Find the indicated

probability.

= 80 = 5

P( x )65 < < 75

P( x )65 < < 75 =

(Round to four decimal places as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

5 of 15 12/1/2016 11:20 PM

5.

6.

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a standard deviation of inches. A study participant is randomly selected. Complete parts (a) through (d) below.

67.3 2.0

(a) Find the probability that a study participant has a height that is less than inches.67

The probability that the study participant selected at random is less than inches tall is . (Round to four

decimal places as needed.)

67

(b) Find the probability that a study participant has a height that is between and inches.67 70

The probability that the study participant selected at random is between and inches tall is . (Round to

four decimal places as needed.)

67 70

(c) Find the probability that a study participant has a height that is more than inches.70

The probability that the study participant selected at random is more than inches tall is . (Round to four

decimal places as needed.)

70

(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

A. The events in parts are unusual because its probabilities are less than 0.05.(a) and (c)

B. The event in part is unusual because its probability is less than 0.05.(a)

C.    than 0.05. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less

D. than 0.05.There are no unusual events because all the probabilities are greater

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of fluid

ounces and a standard deviation of fluid ounce. A drink is randomly selected.

11.6

0.3

(a) Find the probability that the drink is less than fluid ounces.11.4 (b) Find the probability that the drink is between and fluid ounces.11.2 11.4 (c) Find the probability that the drink is more than fluid ounces. Can this be considered an unusual event? Explain your

reasoning.

12

(a) The probability that the drink is less than fluid ounces is .11.4

(Round to four decimal places as needed.)

(b) The probability that the drink is between and fluid ounces is .11.2 11.4

(Round to four decimal places as needed.)

(c) The probability that the drink is more than fluid ounces is .12

(Round to four decimal places as needed.)

Is a drink containing more than fluid ounces an unusual event? Choose the correct answer below.12

A. , because the probability that a drink contains more than fluid ounces is

0.05, this event unusual.

No 12 greater than

is not

B. , because the probability that a drink contains more than fluid ounces is 0.05, this event unusual. Yes 12 greater than

is

C. , because the probability that a drink contains more than fluid ounces is 0.05,

this event unusual.

Yes 12 less than

is

D. , because the probability that a drink contains more than fluid ounces is 0.05, this event unusual. No 12 less than

is not

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

6 of 15 12/1/2016 11:20 PM

7.

8.

The mean incubation time for a type of fertilized egg kept at °F is days. Suppose that the incubation times are approximately normally distributed with a standard deviation of .

100.4 21 2 days

(a) What is the probability that a randomly selected fertilized egg hatches in less than days?19 (b) What is the probability that a randomly selected fertilized egg hatches between and days?17 21

(c) What is the probability that a randomly selected fertilized egg takes over days to hatch?23

(a) The probability that a randomly selected fertilized egg hatches in less than days is .19

(Round to four decimal places as needed.)

(b) The probability that a randomly selected fertilized egg hatches between and days is .17 21

(Round to four decimal places as needed.)

(c) The probability that a randomly selected fertilized egg takes over days to hatch is .23

(Round to four decimal places as needed.)

Use the normal distribution of SAT critical reading scores for which the mean is and the standard deviation is . Assume the variable x is normally distributed.

507 112

(a) What percent of the SAT verbal scores are less than ?675

(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than ?575

Approximately % of the SAT verbal scores are less than .(a) 675

(Round to two decimal places as needed.)

You would expect that approximately SAT verbal scores would be greater than . (Round to the

nearest whole number as needed.)  

(b) 575

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

7 of 15 12/1/2016 11:20 PM

9.

5: Standard Normal Table (Page 1)

The time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.

(a) What waiting time represents the th percentile?20

(b) What waiting time represents the third quartile?

Click to view page 1 of the Standard Normal Table.5

Click to view page 2 of the Standard Normal Table.6

(a) The waiting time that represents the th percentile is days.20

(Round to the nearest integer as needed.)

(b) The waiting time that represents the third quartile is days.

(Round to the nearest integer as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

8 of 15 12/1/2016 11:20 PM

6: Standard Normal Table (Page 2)

z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

3.4− 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003

3.3− 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005

3.2− 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007

3.1− 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010

3.0− 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013

2.9− 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019

2.8− 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026

2.7− 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

2.6− 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047

2.5− 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062

2.4− 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082

2.3− 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107

2.2− 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139

2.1− 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179

2.0− 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228

1.9− 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287

1.8− 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359

1.7− 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446

1.6− 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548

1.5− 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668

1.4− 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 0.0808

1.3− 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968

1.2− 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151

1.1− 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357

1.0− 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587

0.9− 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841

0.8− 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119

0.7− 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420

0.6− 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743

0.5− 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085

0.4− 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446

0.3− 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821

0.2− 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207

0.1− 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602

0.0− 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000

z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

9 of 15 12/1/2016 11:20 PM

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993

3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995

3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

10 of 15 12/1/2016 11:20 PM

10.

7: Standard Normal Table (Page 1)

The time spent (in days) waiting for a kidney transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.

(a) What waiting time represents the th percentile?99

(b) What waiting time represents the first quartile?

Click to view page 1 of the Standard Normal Table.7

Click to view page 2 of the Standard Normal Table.8

(a) The waiting time that represents the th percentile is days.99

(Round to the nearest integer as needed.)

(b) The waiting time that represents the first quartile is days.

(Round to the nearest integer as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

11 of 15 12/1/2016 11:20 PM

8: Standard Normal Table (Page 2)

z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

3.4− 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003

3.3− 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005

3.2− 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007

3.1− 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010

3.0− 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013

2.9− 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019

2.8− 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026

2.7− 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

2.6− 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047

2.5− 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062

2.4− 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082

2.3− 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107

2.2− 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139

2.1− 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179

2.0− 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228

1.9− 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287

1.8− 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359

1.7− 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446

1.6− 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548

1.5− 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668

1.4− 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 0.0808

1.3− 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968

1.2− 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151

1.1− 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357

1.0− 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587

0.9− 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841

0.8− 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119

0.7− 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420

0.6− 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743

0.5− 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085

0.4− 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446

0.3− 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821

0.2− 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207

0.1− 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602

0.0− 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000

z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

12 of 15 12/1/2016 11:20 PM

11.

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993

3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995

3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling

distribution of sample means with sample size n .

= 90 = 12

= 36

(Simplify your answer.) x

=

(Simplify your answer.) x

=

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

13 of 15 12/1/2016 11:20 PM

12.

13.

14.

(1) (c)

(b)

(a)

(2) is the same shape as the graph for the original distribution

approximates a normal curve

The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning.

100

Graph (1) most closely resembles the sampling distribution of the sample means, because

, , and the graph (2) . x

= x

=

(Type an integer or a decimal.)

Find the probability and interpret the results. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialists is about $ . A random sample of

specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $ ? Assume $ .

62,500

30 60,000 = 6,300

The probability that the mean salary of the sample is less than $ is .60,000

(Round to four decimal places as needed.)

Interpret the results. Choose the correct answer below.

A. Only % of samples of specialists will have a mean salary less than $ . This is an event.

14.9 30 60,000 unusual

B. About % of samples of specialists will have a mean salary less than $ . This is not an unusual event.

14.9 30 60,000

C. About % of samples of specialists will have a mean salary less than $ . This is

not an unusual event.

1.49 30 60,000

D. Only % of samples of specialists will have a mean salary less than $ . This is an event.

1.49 30 60,000 unusual

The mean height of women in a country (ages 20 29) is inches. A random sample of women in this age group is selected. What is the probability that the mean height for the sample is greater than inches? Assume .

− 64.4 50 65 = 2.54

The probability that the mean height for the sample is greater than inches is .65

(Round to four decimal places as needed.)

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

14 of 15 12/1/2016 11:20 PM

15.

16.

(1) Yes

No

(2) very unlikely

likely

(3) lies

does not lie

(4) 1 standard deviation

2 standard deviations

3 standard deviations

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents.

The sample mean of the cans is ounces. Does the machine need to be reset? Explain your reasoning. 128 0.40 45

127.9

(1) , it is (2) that you would have randomly sampled cans with a mean equal to

ounces, because it (3) within the range of a usual event, namely within (4) of the mean of the sample means.

45 127.9

(1) accurate

inaccurate

(2) would not

would

(3) lies

does not lie

(4) 1 standard deviation

2 standard deviations

3 standard deviations

(5) No

Yes

(6) lies

does not lie

(7) 1 standard deviation

2 standard deviations

3 standard deviations

A manufacturer claims that the life span of its tires is miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select tires at random and test

them. The mean life span is miles. Assume . Complete parts (a) through (c).

53,000 100

52,854 = 800

(a) Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample is miles or

less?

52,854

(Round to four decimal places as needed.)

(b) Using your answer from part (a), what do you think of the manufacturer's claim?

The claim is (1) because the sample mean (2) be considered unusual since it

(3) within the range of a usual event, namely within (4) of the mean of the sample means.

(c) Assuming the manufacturer's claim is true, would it be unusual to have an individual tire with a life span of miles? Why or why not?

52,854

(5) , because (6) within the range of a usual event, namely within

(7) of the mean for an individual tire.

52,854

Week 5 Homework 40 pts-Jorge Ithier https://xlitemprod.pearsoncmg.com/api/v1/print/math

15 of 15 12/1/2016 11:20 PM