Answer to Question #235840 in Statistics and Probability for Jope

Question

The operations manager of a sugar mill in Chesterville wants to estimate the average size of
an order received. An order is measured in the number of pallets shipped from overseas. A
random sample of 84 orders from customers had a sample mean value of 121.6 pallets.
Assume that the population standard deviation is 20 pallets and that order size is normally
distributed. Estimate, with 92% confidence, the mean size of orders received from all the mill’s
customers (20 marks)

Answer 1

$92\%CI=(121.6-1.74\frac{20}{\sqrt{84}},121.6+1.74\frac{20}{\sqrt{84}})=(117.78,125.42).$

We are 92% confident that the mean size of orders received from all the mill’s customers lies

between 117.78 and 125.42 pallets.