Question

7. Suppose x has a distribution with μ = 29 and σ = 27.

(a) If a random sample of size n = 34 is drawn, find μ_x, σ_x and P(29 ≤ x ≤ 31). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(29 ≤ x ≤ 31) =

(b) If a random sample of size n = 62 is drawn, find μ_x, σ_x and P(29 ≤ x ≤ 31). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(29 ≤ x ≤ 31) =

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is  ---Select--- larger than the same as smaller than part (a) because of the  ---Select--- larger smaller same sample size. Therefore, the distribution about μ_x is  ---Select--- the same narrower wider .

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 78 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 78 tons and standard deviation σ = 0.5 ton.

(a) What is the probability that one car chosen at random will have less than 77.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 16 cars chosen at random will have a mean load weight x of less than 77.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 77.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

YesNo    

Suppose the weight of coal in 16 cars selected at random had an average x of less than 77.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Yes, the probability that this deviation is random is very small.Yes, the probability that this deviation is random is very large.    No, the probability that this deviation is random is very small.No, the probability that this deviation is random is very large.

Answer 1