QUESTION 1: Airline companies recognize that empty seats represent lost revenues
ID: 2907716 • Letter: Q
Question
QUESTION 1: Airline companies recognize that empty seats represent lost revenues that can never be recovered. To avoid losing revenues, the companies often book more passengers than there are available seats. Then, when a flight experiences fewer no-shows than expected, some passengers are 'bumped' from their flights (are denied boarding). Incentives are provided to encourage passengers to give up their reserved seat voluntarily, but occasionally some passengers are involuntarily bumped from the flight. Obviously, these incidents can reflect poorly on customer satisfaction. Suppose Southwest Airlines would like to estimate the true proportion of involuntarily bumped passengers across all domestic flights in the industry. In a pilot sample of 791 domestic passengers, 146 were involuntarily bumped. What is the estimate of the population proportion and what is the standard error of this estimate?
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QUESTION 2: Historically, 78.28% of packages delivered by UPS are on time. Suppose 136 deliveries are randomly selected for quality control. What is the probability that less than 75.56% of the deliveries were on time?
QUESTION 3: You are working as a quality control manager for FedEx and are responsible for delivery time customer satisfaction. Historically, the worldwide average delivery time is 17.2 days with a standard deviation of 6.412 days. You select 57 random deliveries over the course of a few months. Given your historical parameters still hold true, what is the probability that the average time until delivery is between 16.26 and 16.74 days?
QUESTION 4: Fill in the blank. Suppose that NBA players average 24.03 points per game with a standard deviation of 8.673. A random sample of 31 players is taken. There is a 47% chance that the average points per game is greater than ________ points.
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Estimate of proportion: 0.185, Standard error: 0.0005.2)
Estimate of proportion: 0.815, Standard error: 0.0005.3)
Estimate of proportion: 0.815, Standard error: 0.0138.4)
The true population proportion is needed to calculate this.5)
Estimate of proportion: 0.185, Standard error: 0.0138.Explanation / Answer
Solutn1:
estimate of population proportion=sample proportion
=p^
=x/n
=146/791
=0.1845765
p^=0.185
standard error=sqrt(p^(1-p^)/n
=sqrt(0.1845765*(1-0.1845765)/791)
SE =0.0138
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Estimate of proportion: 0.185, Standard error: 0.0138.