The number of minutes late that a flight arrives at an airport is normally distr

Question

The number of minutes late that a flight arrives at an airport is normally distributed with a mean of 8.3 minutes and standard deviation 1.7 minutes. What percentage of flights in this airport are more than 9 minutes late? Suppose we select 10 flights. If each flight can be regarded as a random sample from the population, what percentage of the flights will have an average late between 7.5 minutes and 8.9 minutes? We select 50 flights at random. What is the probability that the average late of these 50 flights will be less than 7.5 minutes? Do the answers of parts (b) and (c) change if the late time of a flight is not normally distributed? Explain why or why not in each case.

Explanation / Answer

1. Here it is given that distribution is normal with mean=8.3 and sd=1.7

a. We need to find P(x>9)=P(z>9-8.3/1.7)=P(z>0.4118)=0.5-P(0<=z<=0.4118)=0.5-0.1598=0.3402

b. Now n=10 and we need to find P(7.5<xbar<8.9)

As population is normal as per Central Limit Theorem mean=mu and sd=sd/sqrt(n)=0.54

So P(7.5-8.3/0.54<z<8.9-8.3/0.54)=P(-1.48<z<1.11)=P(0<=z<=1.11)-P(0<=z<=-1.48)=0.3665+0.4306=0.7971

c. now fior n=50, mean=8.3 and sd=1.7/sqrt(50)=0.24

So P(x<7.5)=P(z<7.5-8.3/0.24)=P(z<-3.33)=0.5+P(0<=z<=-3.33)=0.5-0.4996=0.0004

d. For b it wont be normal as according to Central Limit Theorem n>30 but as for c n=50 it would be normal even though population is not normal.

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