Sampling Distributions of Means

1. An orange juice producer buys all their oranges from one particular orchard. The amount of juice from the oranges is approximately normally distributed with a mean of 141 ml. and a standard deviation of 44 ml. What is the probability that 8 oranges will provide enough juice to fill a 1 litre container?

2. The occurrence of the first breakdown of an automatic washing machine is normally distributed with a mean of 5.7 years and a standard deviation of 8 years. How long (full years) should these washing machines be guaranteed so that no more than 8 % would require repairs during the warrantee period?

5. To check the Ace company's claim that the total of their 2,300 accounts receivable was $1,104,000 and that the standard deviation of the individual accounts was $ 180 the external auditor took a sample of 25 accounts which totalled $10,150.

a) If the company's report is correct, what is the probability that the average balance of an account in the sample is $400 or less?

b) If the total of the accounts receivable is only $1,000,000 (but the standard deviation was correct), what is the probability the total of the sample would be less than $10,150