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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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MATH1123, section OB, Fall 2023

Chapter 6 homework (Homework) INSTRUCTOR

Hua He

Hawaii Paci�c University

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SUN, NOV 19, 2023

11:59 PM HST

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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State whether each of the following random variables is discrete or continuous.

(a) the number of defective tires on a car

(b) the body temperature of a hospital patient

(d) the number of draws (with replacement) from a deck of cards until a heart is selected

(e) the length of a movie

discrete

continuous

discrete

continuous

discrete

continuous

discrete

continuous

discrete

continuous

1. [5/5 Points] PECKSTAT3 6.1.001.DETAILS PREVIOUS ANSWERS

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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Consider the random variable y = Number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows.

y 0 1 2 3 4

p(y) 0.64 0.19 0.11 0.05 ?

(a) Only y values of 0, 1, 2, 3, and 4 have probabilities greater than 0. What is p(4)?

.01

(b) How would you interpret p(1) = 0.19?

Interpret this probability.

If you check a large number of cartons, the proportion that will have at most two broken eggs will equal this value.

The proportion of eggs that will be broken in any two cartons from this population is this value.

The probability of two randomly chosen cartons having broken eggs in them is this value.

In the long run, the proportion of cartons that have exactly two broken eggs will equal this value.

(d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs.

Why is this smaller than the probability in part (c)?

This probability is not less than the probability in part (c) because the two probabilities are the same for this distribution.

This probability is less than the probability in part (c) because the proportion of eggs with any exact number of broken eggs is negligible.

This probability is less than the probability in part (c) because the event y = 2 is now not included.

This probability is less than the probability in part (c) because in probability distributions, P(y ≤ k) is always greater than P(y < k).

(e) What is the probability that the carton contains exactly 10 unbroken eggs?

(f) What is the probability that at least 10 eggs are unbroken?

The proportion of eggs that will be broken in each carton from this population is 0.19.

In the long run, the proportion of cartons that have exactly one broken egg will equal 0.19.

If you check a large number of cartons, the proportion that will have at most one broken egg will equal 0.19.

The probability of one randomly chosen carton having broken eggs in it is 0.19.

2. [2/8 Points] PECKSTAT3 6.2.010.DETAILS PREVIOUS ANSWERS

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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.96

Suppose that fundraisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year's graduates.

Size of donation $0 $10 $25 $50

Proportion of calls 0.40 0.30 0.25 0.05

Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Consider the variable of donation for a person selected at random from the population of last year's graduates of this university.

(a) Write a few sentences describing what donation amounts you would expect to see if the value of x was observed for each of 1,000 graduates.

You would expect roughly of the graduates to donate nothing, roughly to donate $10, roughly

to donate $25, and roughly to donate $50. The frequencies would be close to, but not exactly,

these values. The four frequencies would add to .

(b) What is the most common value of x in this population?

(d) What is

x = Amount

P(x ≥ 25)?

P(x > 0)?

3. [–/8 Points] PECKSTAT3 6.2.011.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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A business has six customer service telephone lines. Consider the random variable x = Number of lines in use at a randomly selected time. Suppose that the probability distribution of x is as follows.

x 0 1 2 3 4 5 6

0.05 0.10 0.20 0.35 0.20 0.08 0.02

(a) Calculate the mean value and standard deviation of x. (Round your standard deviation to four decimal places.)

(b) What is the probability that the number of lines in use is farther than 3 standard deviations from the mean value?

p(x)

𝜇x

𝜎x

4. [–/3 Points] PECKSTAT3 6.4.040.MI.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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The probability distribution of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station, is given in the following table.

x 0 1 2 3 4

0.51 0.17 0.07 0.04 0.21

The mean value of x is Calculate the values of and (Round your answers to four decimal places.)

Interpret the value of

This value measures the long-run average number of tires needing replacement.

This value measures the long-run average number of tires needing replacement relative to the mean.

This value measures the square of how much, on average, the number of tires needing replacement deviates from the mean.

This value measures how much, on average, the number of tires needing replacement deviates from the mean.

This value measures the square root of how much, on average, the number of tires needing replacement deviates from the mean.

Interpret the value of

This value measures the long-run average number of tires needing replacement.

This value measures the long-run average number of tires needing replacement relative to the mean.

This value measures the square of how much, on average, the number of tires needing replacement deviates from the

mean.

This value measures how much, on average, the number of tires needing replacement deviates from the mean.

This value measures the square root of how much, on average, the number of tires needing replacement deviates from the mean.

p(x)

𝜇 = 1.27.x 𝜎x 2

𝜎 .x

𝜎x 2

𝜎x

𝜎 .x 2

𝜎 .x

5. [–/4 Points] PECKSTAT3 6.4.038.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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Determine the following standard normal (z) curve areas. (Round your answers to four decimal places.)

(a) the area under the z curve to the left of 1.74

(b) the area under the z curve to the left of

(d) the area under the z curve to the right of

(e) the area under the z curve between and 0.56

(f) the area under the z curve between and 2

(g) the area under the z curve between and 4

−0.66

−2.83

−2.23

−2

−4

6. [–/7 Points] PECKSTAT3 6.5.041.MI.S.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm. (Round your answers to four decimal places.)

(a) What is the probability that a randomly selected typist's speed is at most 60 wpm?

What is the probability that a randomly selected typist's speed is less than 60 wpm?

(b) What is the probability that a randomly selected typist's speed is between 30 and 75 wpm?

It ---Select--- be surprising to find a typist in this population whose speed exceeded 105 wpm because the probability

of finding such a typist is only .

(d) Suppose that two typists are independently selected. What is the probability that both their speeds exceed 90 wpm?

(e) Suppose that special training is to be made available to the slowest 15% of the typists. What typing speeds (in wpm) would qualify individuals for this training?

Any typist with a typing speed of wpm or less is in the slowest 15% of typists.

†

7. [–/7 Points] PECKSTAT3 6.5.044.S.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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A certain paper suggested that a normal distribution with mean 3,500 grams and standard deviation 530 grams is a reasonable model for birth weights of babies born in Canada. (Round your answers to four decimal places.)

(a) One common medical definition of a large baby is any baby that weighs more than 4,000 grams at birth. What is the probability that a randomly selected Canadian baby is a large baby?

(b) What is the probability that a randomly selected Canadian baby weighs either less than 2,000 grams or more than 4,000 grams at birth?

Any baby with a weight of grams or more is in the greatest 20% of birth weights.

8. [–/3 Points] PECKSTAT3 6.5.051.S.DETAILS MY NOTES PRACTICE ANOTHER

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11/17/23, 10:29 PM Chapter 6 homework - MATH1123, section OB, Fall 2023 | WebAssign

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Determine the following areas under the standard normal (z) curve. (Round your answers to four decimal places.)

(a) to the left of

(b) to the right of 1.29

(d) to the right of 0

(e) to the right of

(f) between and 2.6

(g) to the left of 0.21

Home My Assignments

−1.29

−1

−5

−1.7

9. [–/7 Points] PECKSTAT3 6.5.047.MI.S.DETAILS MY NOTES PRACTICE ANOTHER

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