An insurance company wants to audit health insurance claims in
its very large database of transactions. In a quick attempt to
assess the level of overstatement of this database, the insurance
company selects at random 400 items from the database (each item
rep- resents a dollar amount). Suppose that the population mean of
the entire database is $8, with population standard deviation
$2.
(i) Find the probability that the sample mean of the 400 would
be less than $6.50.
(ii) Why can we use the normal distribution in obtaining an
answer to part (i)?
(iii) For what value of e can we say that P(8 - e < X
< 8 + e) is equal to 90%?