The monthly expenditures on food by single adults in one cit

The monthly expenditures on food by single adults in one city are normally distributed with amean of $410 and a standard deviation of $70. What is the probability that the sampling error madein estimating the mean monthly expenditure of all single adults in that city by the mean of arandom sample of 90 such adults will be at most $10?

Solution

z= (420-410)/70= 0.14
The probability of 0.14 standard deviations above or below the mean is (from a normal curve table) .5557-.4443=0.1114