Mind on Statistics
Mind on Statistics
5th Edition
ISBN: 9781285463186
Author: Jessica M. Utts, Robert F. Heckard
Publisher: Brooks Cole
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Chapter 7, Problem 7.1E
To determine

To indicate: The given situation in terms of a random circumstance and the related probability.

Expert Solution & Answer
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Answer to Problem 7.1E

Whether the domestic flight is late or not late will be a random circumstance here. The probability of the flight arriving on time is 0.787, and the probability of the flight being late is 0.213.

Explanation of Solution

Given information:

According to the website, 78.7% of the flights of the top 18 airlines are not late.

Concept used:

Any situation where the outcome is unexpected is said to be a random circumstance. In many situations, the result is not known until after it is observed or visible.

In this case, the requirement is to represent the term in random circumstances. There can be two possible cases for any random event, whether the flight is on time or not on time.

As it is mentioned on the website that 78.7% of the flights of the top 18 airlines are not late, it can be concluded that there is a 0.787 probability that the flight will not be late. There may be another case too. The probability that the flight will not be on time is 0.213.

Therefore, the random circumstance for this case will be the domestic flight is not late, or the flight is late. The probability the flight is on time is 0.787, and the probability of arriving on the flight late is 0.213.

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To  evaluate  the  success  of  a  1-year  experimental  program  designed  to  increase  the  mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year’s  statewide  average  of  525  for  underprivileged  seniors.  The  researchers  want  to  determine  whether the experimental program has increased the mean achievement level over the previous year’s statewide average. If alpha=.05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, sigma=80.
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