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Chapter 7 Homework
Question 1: What is the mean, standard deviation, and sample size?
Mean= 4 hours
Standard deviation= 1.2 hours
Sample size = 16 employees
Question 2: Complete the distribution.
a) X ~ N (4, 1.2)
b) U (1.2, 16)
Question 3: Find the probability that one review will take Yoonie from 3.5 to 4.25
hours.
a)
b) P(3.5<x<4.25)
= z1 = (x- u)/ standard deviation
= (3.5 – 4)/ 1.2
= (4.25 – 4)/ 1.2
= - 0.4167; 0.2084
P( -0.4167 <z < 0.2084)
P(3.5<x<4.25) = 0.2441
Question 17: Find the probability that the sum of the 100 values is less than 3,900.
Mean = 39.01; standard deviation= 0.5
Mean sums = (n)(x) = 39.01* 100= 3901
P (Σx < 3900) = 0.4207
Question 19: Find the sum of a z- score of -2.5
Z = (x – mean)/ sd
-2.5 = (x – 39.01)/ 0.5
X = (-1.25) – 39.01
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X = 37.76* 100
X = 3776
Question 25: What is P (Σx > 290)?
Mean = 12; sd = 1 n = 25
= 12(25) = 300
= 1(25) = 25
Therefore, P (Σx > 290) = 0.9772
Question 29: An unknown distribution has a mean of 25 and a standard deviation
of six. Let X = one object from this distribution. What is the sample size if the
standard deviation of ΣX is 42?
Mean = 25; sd = 6
42= (√n)(σx)
√n = 42/ 6
N= 7)**2
N = 49
Question 34: What is the mean of ΣX?
ΣX = 100*100
= 10,000
Question 58: Find the first quartile for the sums
(6< x< 10); N = 50
a= 6; b = 10
mean = (16)/ 2 = 8
sd = sqrt ((10 – 6)^2) / 12
sd = 1.1547
sum x = N( 50*8, (50**2)(1.1547)
N(400, 8.13)
Z = 1.29
1.29 = (q1 – 400)/ 8.13
10.48 = q1 – 400
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Q1 = 410.49
Question 64: Suppose that a category of world-class runners is known to run a
marathon of 26 miles in an average of 145 minutes with a standard deviation of
14 minutes. Consider 49 of the races. Let me of average of the races 49 races
This is the average number of minutes taken in the race.
80th percentile; 0.8
Z score = 0.78814
Mean = 49 marathons
Sd = 14
0.78814 = (x – 49)/ 98
77.224 = x – 49
X = 126.2 a
Question 65: The length of songs in collectors’ iTunes album collection is uniformly
distributed from two to 3.5 minutes. Suppose we randomly pick five albums from
the collection. There are a total of 43 songs on the five albums
a) The length of a song, in minutes in the collection
b) U (2, 3.5)
c) The average length in minutes of the songs from a sample of five albums from
the collection
d) Z= (x – mean)/ sd/ sqrt (n)
-0.675= (q1 – 2.75)
Q1 = 2.706
e) IQR = Q3 – Q
= 2.794 – 2.706
= 0.088
Question 66: In 1940 the average size of a US farm was 174 acres. Let’s say that
the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from
1940
a) The size of farms in acres
b) The average length of farms from the sample of 38 farmers selected
c) U (
d) Z = (136 – 174)/ 55
Z = - 0.690
Q1 = 0,2451
Question 67: Determine which of the following is true and which is false, then
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a) True the mean of a sampling distribution of the means is approximately the
mean of the data
b) True. The larger the sample the closer the sampling distribution of the means
becomes normal according to central limit theorem.
c) The standard deviation of the sampling distribution of the means will decrease
making it approximately the same as the standard deviation of x as the sample
size increases.
Question 52: Find the 80th percentile for the total length of time 64 batteries last
Question 73: Suppose that the duration of a particular type of criminal trial is
known to have a mean of 21 days and a standard deviation of seven days. We
randomly ample nine trials
a) The total number of days for nine trials
b) N (189, 21)
c) 0.0432
d) 162.09; ninety percent of the total nine trials of this type will last 162 days or
more.
Question 81: The 90th percentile sample average wait time (in minutes) for a
sample of 100 riders is:
90th percentile =0.9
= (75 -0)/ 2 = 37.5
Standard deviation = sqrt ((75- 0) **2)/ 10 = 2.2
invNorm (0.90, 37,5, 2.2)
= 40.3
Question 83: What’s the approximate probability that the average price for 16 gas
stations is over $ 4.69?
Mean = 4.59; 4.69
Sd = 0.01
X = 16
Z scores= (16 -4.59)/ 0.10 = 1.141
Z score = (16 -4.69)/ 0.10 = 1.113
Probability = 0.87286 – 0.87076
Probability = 0.0021 which is almost zero
Question 33: is P (Σx < 1,186)?
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Mean sum= 400 *3 = 1200
Mean sd = sqrt 0.7 * 400 = 334.66
= normal cdf (1186, e99, (0.7* 334.66)
= 0.15868
Question 34: What is the mean of x?
Mean = 100; sd = 100; n =100
X = 1
Mean sum of x = (100*100)
Mean sum of x = 10,000
