Mean, standard deviation and random probability

Question

The mean one-way commute to work in New York City is 38.3 minutes. The Standard deviation is 7.5 minutes. What is the probability of randomly selecting one commute time and finding that:

a). P (× < 30 minutes)

b). P (× > 40 minutes)

c). P (x > 30 minutes)

d). P (x < 40 minutes)

e). P (32 < × > 42 minutes)

f). P (30 < × < 32 minutes)

g). P (40 < × < 42 minutes)

h). Info... Based on the previous info, the New York City Transportation Dept. Manager wants to test to see if the goal that at least 68℅ of the one-way work commutes in NYC are less than 46.5 minutes is being met. Is this goal being not met, exactly met, or exceeded? Please show applicable computations, including a drawing of the normal probability distribution for each individual problem.

(Clue: The goal is not being successfully met but is being exceeded).

Answer 1

a). P (× < 30 minutes) Answer: 0.1335

b). P (× > 40 minutes) Answer:0.409

c). P (x > 30 minutes) Answer: 0.8665

d). P (x < 40 minutes) Answer: 0.591

e). P (32 < × > 42 minutes) Answer: 0.4874

f). P (30 < × < 32 minutes) Answer: 0.067

g). P (40 < × < 42 minutes) *try on your own, apply the same concepts

h.) Not sure of correct answer