Question

mong the thirty largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. The longest one-way travel time is in New York City, where the mean time is 38.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.7 minutes. Use Appendix B.3

. What percent of the New York City commutes are for less than 27 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

What percent are between 27 and 35 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

What percent are between 27 and 43 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

Answer 1

Since the distribution is normal hence to find the probability, Z score is applicable here so,

a) Since, mean time is 38.8 minutes and standard deviation, S is 7.7 minutes, by Z score at 27

So, P(X<27)= P(Z<-1.532) which is computed using the Z table shown below or by excel tool as

The P-Value is 0.06

b). To find P(27<X<35) Z values at 27 and 35 need to be calculated as

at X=27

and at X=35

So, P(27<X<350=P(-1.532<Z<0.494)

hence, 0.3106-0.0628

=0.25

c)Again to find P(27<X<43) Z values is calculated

and At X= 43

So, P(27<X<43)=P(-1.532<Z<0.546)

=0.7075-0.0628

=0.65