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Chapter 6: Q. 104 (page 430)

In debt? Refer to Exercise 100.

a. Justify why D can be approximated by a normal distribution.

b. Use a normal distribution to estimate the probability that 30or more adults in the sample have more debt than savings.

Short Answer

Expert verified
  1. The D is about regularly distributed
  2. The resultant probability is0.08

Step by step solution

01

Part (a) Step 1: Given Information

Given:

Adult population is (n)=100

The percentage of adults who owe more money than they saverole="math" localid="1653979441143" (p)=0.24

02

Part (a) Step 2: Check that D is generally distributed for a reason.

Consider,

np=100(0.24)=24>10n(1-p)=100(1-0.24)=76>10

Therefore, the D is about regularly distributed.

03

Part (b) Step 1: Given Information

Given:

Adult population isn=100

The percentage of adults who owe more money than they save(p)=0.24

04

Part (b) Step 2: calculate the likelihood that at least 30 persons in the sample have more debt than savings.

When 30 or more adults have more debt than savings, the likelihood is computed as follows:

P(X鈮�30)=PZ鈮�30-100(0.24)100(0.24)(1-0.24)=P(Z鈮�1.405)=1-0.920=0.08

As a result, a probability of 0.08 is necessary.

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Most popular questions from this chapter

Quick, click! An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject clicks 鈥淪tart.鈥� The density curve models the amount of time Y (in seconds) that the subject has to wait for the light to flash.

a) Find and interpret P(Y>3.75)

b) What is 渭Y? Explain your answer.

c) Find the value of k that makes this statement true:P(Y鈮�k)=0.38

Take a spin Refer to Exercise 83. Calculate and interpret P(X鈮�7)

Take a spin An online spinner has two colored regions-blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner12 times and let X= the number of times it lands in the blue region. Make a graph of the probability distribution of X. Describe its shape.

.Essay errors Typographical and spelling errors can be either 鈥渘onword errors鈥� or 鈥渨ord errors.鈥� A nonword error is not a real word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� A word error is a real word, but not the right word, as when 鈥渓ose鈥� is typed as 鈥渓oose.鈥� When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X has the following probability distribution:

Value of X01234
Probability0.10.20.30.30.1

渭X=2.1蟽X=1.136

Value of Y0123
Probability0.40.30.20.1

渭Y=1.0蟽Y=1.0

a) Find the mean and standard deviation of the difference Y-Xin the number of errors made by a randomly selected student. Interpret each value in context.

(b) Challenge: Find the probability that a randomly selected student makes more word errors than nonword errors .

If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?

a. 0.25

b. 1.00

c. (41)(0.25)3(0.75)341(0.25)3(0.75)3

d. (41)(0.25)1(0.75)341(0.25)1(0.75)3

e.(0.75)3(0.75)1
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