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Chapter 4: Q.128 (page 299)

In words, the random variableX=_________________

a. the number of times Mrs. Plum鈥檚 cats wake her up each week.

b. the number of times Mrs. Plum鈥檚 cats wake her up each hour.

c. the number of times Mrs. Plum鈥檚 cats wake her up each night.

d. the number of times Mrs. Plum鈥檚 cats wake her up.

Short Answer

Expert verified

Answer of all parts a,b,c,d is

The number of times Mrs. Plum's cats wake up each week is represented by the Random variable X.

Step by step solution

01

Introduction

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable might be discrete (meaning it has definite values) or continuous (meaning it has no specific values) (any value in a continuous range)

02

Explanation (a)

Mrs. Plum's cats wake her up on average 10 times every week.

X is a Random variable that indicates the number of times per week that Mrs. Plum's cats wake up.

03

Explanation (b)

Mrs. Plum's cats wake her up on average 10 times every week.

X is a Random variable that indicates the number of times per week that Mrs. Plum's cats wake up.

04

Explanation (c)

Mrs. Plum's cats wake her up on average 10 times every week.

X is a Random variable that indicates the number of times per week that Mrs. Plum's cats wake up.

05

Explanation (d)

Mrs. Plum's cats wake her up on average 10 times every week.

X is a Random variable that indicates the number of times per week that Mrs. Plum's cats wake up.

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Most popular questions from this chapter

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

X~_____(_____,_____)

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many instructors do you expect on the committee who are not technically proficient?

e. Find the probability that at least five on the committee are not technically proficient.

f. Find the probability that at most three on the committee are not technically proficient.

A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let X = the number of times a patient rings the nurse during a 12-hour shift. For this exercise, x = 0, 1, 2, 3, 4, 5. P(x) = the probability that X takes on value x. Why is this a discrete probability distribution function (two reasons)?

The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate in Afghanistan is 28.1%. Suppose you choose 15 people in Afghanistan at random. Let X = the number of people who are literate.

a. Sketch a graph of the probability distribution of X.

b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X.

c. Find the probability that more than five people in the sample are literate. Is it is more likely that three people or four people are literate.

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon.

a. Find the mean and standard deviation of X.

b. What is the probability that the office receives at most six calls at noon on Monday?

c. Find the probability that the law office receives six calls at noon. What does this mean to the law office staff who get, on average, 5.5 incoming phone calls at noon?

d. What is the probability that the office receives more than eight calls at noon?
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