Question

Among 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 38.5 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes. Use Appendix B.3.

1. What percent of the New York City commutes are for less than 26 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

2. What percent are between 26 and 34 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

3. What percent are between 26 and 45 minutes? (Round your intermediate calculations and final answer to 2 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 38.5

standard deviation = = 7.2

a ) P(x < 26 ) = P[(x - ) / < (26 - 38.5) /7.2 ]

= P(z < -1.74)

=0.0409

probability = 0.0409

b)

P(26 < x < 34) = P[(26-38.5)/7.2 ) < (x - ) /  < (34 - 38.5) /7.2 ) ]

= P(-1.74 < z < -0.625 )

= P(z < -0.63) - P(z < -1.74 )

= 0.2643 - 0.0409

= 0.2234

probability =0.2234

c )

P(26 < x < 45) = P[(26-38.5)/7.2 ) < (x - ) /  < (45 - 38.5) /7.2 ) ]

= P(-1.74 < z < 0.90)

= P(z < 0.90) - P(z < -1.74 )

= 0.8159 - 0.0409

= 0.7750

probability =0.7750