Question

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 51 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 51 tons and standard deviation σ = 1.3 ton.

(a) What is the probability that one car chosen at random will have less than 50.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 21 cars chosen at random will have a mean load weight x of less than 50.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 50.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

YesNo    

Suppose the weight of coal in 21 cars selected at random had an average x of less than 50.5 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.

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 38 minutes and standard deviation σ = 6 minutes. (Round your answers to four decimal places.)

(a) What is the probability that a first interview will last 40 minutes or longer?


(b) Fifteen first interviews are usually scheduled per day. What is the probability that the average length of time for the fifteen interviews will be 40 minutes or longer?

Find P(33 ≤ x ≤ 38). (Round your answer to four decimal places.)

Answer 1

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