Answer to Question #248072 in Statistics and Probability for Sharon

Question

1.           The distance traveled per taxi per year is normally distributed with a mean of 40 thousand miles and a variance of 169 thousand miles. Compute the probability of taxi can be expected to travel:

 

a.           between 30 and 70 thousand miles in a year.

[4 marks]

 

b.           above 60 thousand miles in a year.(3 marks)

                       

c.            above 27 thousand miles in a year.

[3 marks]

Answer 1

N(40,169) = 40 + 13Z(0,1)

So, the task is to calculate next probabilities:

(a) P(30 < 40+13Z(0,1) < 70) = P(Z(0,1) < 2.3) - P(Z(0,1) < -0.77) = 0.9893 - 0.2206 = 0.7687

(b) P(40+13Z(0,1) > 60) = P(Z(0,1) > 1.54 = 0.0618

(c) P(40+13Z(0,1) > 27) = P(Z(0,1) > -1) = 0.8413