A trucking company determined that the distance traveled per truck per year is n

Question

A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 80 thousand miles and a standard deviation of 12 thousand miles. Complete parts (a) through (c) below. a. What proportion of trucks can be expected to travel between 64 and 80 thousand miles in a year? The proportion of trucks that can be expected to travel between 64 and 80 thousand miles in a year is 4088 (Round to four decimal places as needed.) b. What percentage of trucks can be expected to travel either less than 55 or more than 95 thousand miles in a year? The percentage of trucks that can be expected to travel either less than 55 or more than 95 thousand miles in a year is (Round to two decimal places as needed.)

Explanation / Answer

b) Probailty = 1 - P(55 < X < 95)

                   = 1 - P((55 - ) / < Z < (95 - ) / )

                   = 1 - P((55 - 80) / 12 < Z < (95 - 80) / 12)

                   = 1 - P(-2.08 < Z < 1.25)

                   = 1 - [P(Z < 1.25) - P(Z < -2.08)]

                   = 1 - (0.8944 - 0.0188)

                   = 0.1244

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