Apex Machinery manufactures large earth-moving equipment. Their sales for a part

Question

Apex Machinery manufactures large earth-moving equipment. Their sales for a particular machine had been averaging $450,000/month with a standard deviation of $100,000. 36 months ago, they were forced to recall some machines because of a safety defect. For the 36 months since the recall their sales have averaged $370,000. (Sales were nonseasonal and the 36 months can be assumed to be a random sample).

. What is the probability of Apex’s average sales being between $370,000 and $400,000 if the recall had no effect on their true average sales?

Explanation / Answer

we can assume normal distirbution for sample size is greater than 30,

for normal distribution z score =(X-)/ here mean=       = 450000.000 std deviation   == 100000 sample size       =n= 36 std error=x=/n= 16666.6667 probability = P(370000<X<400000) = P(-4.8<Z<-3)= 0.0013-0= 0.0013

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