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Chapter 7: Q. 71 (page 481)

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

Short Answer

Expert verified

The required value isP(X¯≥200)=5.94%

Step by step solution

01

Given information 

Given,

μ=190σ=35n=30∑xi=6000
02

Calculation

Formula used:

z=x-μσ

Lets calculate,

localid="1657630239006" x¯=∑xin=600030=200z=x¯-μx¯σx¯=x¯-μσln=200-19035/30≈1.56P(X¯≥200)=P(Z>1.56)=1-P(Z>1.56)=1-0.9406=0.0594=5.94%

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Most popular questions from this chapter

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution ofx-x¯ to be 10 seconds? Justify your answer.

Dem bones (2.2) Osteoporosis is a condition in which the bones become brittle due to the loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in a standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is 2.5standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.

a. What percent of healthy young adults have osteoporosis by the WHO criterion?

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a. Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds 55 .\(

b. What are the mean and standard deviation of the sampling distribution of x-x¯?

c. What is the shape of the sampling distribution of x-x¯? Justify your answer.

d. Find the probability that the average fee paid by the sample of households exceeds 55 .\)


On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?

a. All people who have ever listened to this show

b. All people who listened to this episode of the show

c. All people who visited the show host's website

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In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

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e. approximately Normal with mean 122 and standard deviation 0.35.
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