Question

The mean of the distribution of truck weights is 20,000 lbs with a standard deviation of 2,000 lbs. Assume that the distribution approximates a Bell curve.

Suppose you pick a single truck at random. What is the probability that the weight will be between 21,000 and 22,000 miles? Use area from a value. (Show a screen shot for your answer.)

Use the central limit theorem to the following questions.

Suppose you pick a group of 16 trucks instead. What would be the standard deviation of the sample’s (group’s) average? (i.e. σxbar = σ/√n)

What is the probability that a group of 16 trucks will have an average weight between 21,000 and 22,000 miles?

Use the z-table calculator with “area from a value”. (Show a screen shot for your answer.)

Answer 1

mean = 20000 , s = 2000 , n = 16

P(21000 < x < 22000)
= P((21000- 20000)/(2000/sqrt(16)) < z < ((22000- 20000)/(2000/sqrt(16))

= P(2 < z < 4)
= P(z< 4) - P(z< 2)
= 1 -0.9772
= 0.0227