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 62 and 80 thousand miles in a year? The proportion of trucks that can be expected to travel between 62 and 80 thousand miles in a year is 0.4332 (Round to four decimal places as needed.) b. What percentage of trucks can be expected to travel either less than 70 or more than 95 thousand miles in a year? The percentage of trucks that can be expected to travel either less than 70 or more than 95 thousand miles in a year is L%. (Round to two decimal places as needed.) C. How many miles will be traveled by at least 85% of the trucks? The amount of miles that will be traveled by at least 85% of the trucks is miles. (Round to the nearest mile as needed.)

Explanation / Answer

solution :

Given that mean ? = 80 , standard deviation ? = 12

a. P(62 < x < 80) = P((x - ?)/? < Z < (x - ?)/?)

= P((62 - 80)/12 < Z < (80 - 80)/12)

= P(-1.5 < Z < 0)

= 0.4332

b. P(x < 70) + P(x > 95) = P(Z < (70 - 80)/12) + P(Z > (95 - 80)/12)

= P(Z < -0.8333) + P(Z > 1.25)

= 0.2033 + 0.1056

= 0.3089

= 30.89%

c. Let d be the number of miles at least 85% of the trucks will travel

=> P(x >= d) = 0.85

=> P(x < d) = 0.15

=> P(Z < (d - 80)/12) = 0.15

=> (d - 80)/12 = -1.0364

=> d = -1.0364*12 + 80

= 67.5632

= 68 (nearest integer)

=> the amount of miles that will be traveled by atleast 85% of the trucks is 68 miles

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.