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 75 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 75 tons and standard deviation σ = 0.6 ton.

(a) What is the probability that one car chosen at random will have less than 74.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 46 cars chosen at random will have a mean load weight x of less than 74.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes

No    

Suppose the weight of coal in 46 cars selected at random had an average x of less than 74.5 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

Solution :

Given that,

mean = = 75

standard deviation = = 0.6

a ) P( x < 74.5 )

P ( x - / ) < ( 74.5 - 75 / 0.6)

P ( z < -0.5 / 0.6 )

P ( z < - 0.83)

= 0.2033

Probability = 0.2033

b ) n = 46

= 75

₌ / n =0.6 46 = 0.0885

P( x < 74.5 )

P ( x - / ) < ( 74.5 - 75 / 0.0885)

P ( z < -0.5 / 0.0885 )

P ( z < - 5.65)

= 0

Probability = 0

c ) Yes

Yes, the probability that this deviation is random is very large