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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

A small ferry runs every half hour from one side of a large river to the other. The number of cars Xon a randomly chosen ferry trip has the probability distribution shown here with mean 渭X=3.87and standard deviation 蟽X=1.29. The cost for the ferry trip is $5. Define M=money collected on a randomly selected ferry trip.

a. What shape does the probability distribution of Mhave?

b. Find the mean of M.

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randomly selected horse pregnancy.

a. Write the event 鈥減regnancy lasts between 325 and 345 days鈥� in terms of X. Then find

this probability.

b. Find the value of c such thatP(X鈮�c)=0.20

During the winter months, the temperatures at the Starneses鈥� Colorado cabin can stay well below freezing (32掳For0掳C)for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50掳F.She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years鈥� worth of data, the temperature Tin the cabin at midnight on a randomly selected night can be modeled by a Normal distribution with mean 8.5掳Cand standard deviation 2.25掳C. Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall thatF=(9/5)C+32).

a. Find the mean of Y.

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c. Find the probability that the midnight temperature in the cabin is less than 40掳F.

Fire insurance Suppose a homeowner spends \(300 for a home insurance policy that will pay out \)200,000 if the home is destroyed by fire in a given year. Let P = the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is 0.0002.

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Baby elk Refer to Exercise 77 . Use the binomial probability formula to find P(X = 4) . Interpret this value.
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