QUESTION 1

a. A car battery manufacturer claims that its Power-Eriz battery type has a mean lifetime of 60,000 miles. Suppose that the lifetimes are normally distributed with a standard deviation of 3,500 miles. A consumer group buys FIVE (5) such battery and tests them.

i. Find the probability that the average lifetime of the five batteries will be less than 57,000 miles.

ii. From the probability calculated in (i) is the battery is as good as claimed? Give your reason.

b. Best Property Management estimated that 55% of its individual investment accounts are female. If 25 individual investment accounts are selected randomly,

i. what is the distribution of the sample proportion (? Justify your answer.

ii. what is the probability that the individual investment account is female more than 60%?

iii. exactly 55% of the individual investment account is female?