The times spent waiting in line by all drivers to get their licenses renewed at

Question

The times spent waiting in line by all drivers to get their licenses renewed at the motor vehicle department office of a large city have a distribution that is skewed to the right with a mean of 24 minutes and a standard deviation of 7 minutes.

Calculate the mean and standard deviation of x and comment on its shape of its sampling distribution and why its isthat shape.

Find the probability that the mean waiting time for a random sample of 100 drivers to get their licenses renewed is:

a. less than 22 minutes

b. between 23-26 minutes

c. within 2 minutes of population mean

d. greater than the population mean by 4 minutes

Explanation / Answer

for n=100 ; mean =24

std deviation of mean =7/(100)1/2 =0.7

ffor sample size is greater then 30 ; therefore as per central limit theorum shape of the distribution will be normal.

a) P(X<22) =P(Z<(22-24)/0.7)=P(Z<-2.8571)=0.0021

b)P(23<X<26)=P(-1.4286<Z<2.8571)=0.9979-0.0766 =0.9213

c)P(22<X<26)= P(-2.8571<Z<2.8571)=0.9979-0.0021 =0.9957

d)P(X>28)=1-P(X<28)=1-P(Z<5.7143)=1-~1 =0.0000

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