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Chapter 5: Q. 94. (page 347)

Late flights An airline reports that 85% of its flights arrive on time. To find the

probability that a random sample of 4 of this airline’s flights into LaGuardia Airport in New York City on the same night all arrive on time, can we multiply (0.85)(0.85)(0.85)(0.85)? Why or why not?

Short Answer

Expert verified

No, because the provided events cannot be considered independent events

Step by step solution

01

Given information

P(Flight arrives on time)=85%=0.85
P(All flights are on time)=0.5220

02

Explanation

The probability of flights arriving on time is not independent, which means that if one flight is delayed, another flight may also be delayed as a result of the first flight's delay. Because the events are not self-contained. As a result, the results are incorrect because they were calculated using the multiplication rule, which is only used in the case of independent events.

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The security system in a house has two units that set off an alarm when motion is

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assumes that the next card dealt in the same hand is equally likely to be red or black.

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Lefties A website claims that 10%of U.S. adults are left-handed. A researcher believes that this figure is too low. She decides to test this claim by taking a random sample of 20U.S. adults and recording how many are left-handed. Four of the adults in the sample are left-handed. Does this result give convincing evidence that the website’s 10%claim is too low? To find out, we want to perform a simulation to estimate the probability of getting 4or more left-handed people in a random sample of size 20from a very large population in which 10%of the people are left-handed.

Let 00to 09indicate left-handed and 10to 99 represent right-handed. Move left to Page Number: 311right across a row in Table D. Each pair of digits represents one person. Keep going until you get20 different pairs of digits. Record how many people in the simulated sample are left-handed. Repeat this process many, many times. Find the proportion of trials in which4 or more people in the simulated sample were left-handed.
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