Question

You own a retail store that has problems with shoplifting. Each day, the expected value of the amount stolen is $300, with a standard deviation of $30. You try hiring a security guard for 100 days. Let X be the average amount stolen on those 100 days. Assume that the standard deviation of the amount stolen each day was unaffected, but that the expected value of the amount stolen on any given day could be affected. Page 1 Professor Timothy Rocper Statistics Midterm 2 Name: (a) (5 points) Find o (b) (9 points) For those 100 days, the average amount stolen was just $197. Find a 90% confidence interval for the expected value of the amount stolen on days with a security guard (c) (9 points) You have the option of hiring the security guard for $106/day. What is the probability that this will save you money?

Answer 1

For the question it is given that

Mean,m= $197,standard deviation,s =$30 and sample size,n = 100

We have been given the population standard deviation, therefore we will use z-score to calculate the confidence interval.

z critical value using 90% confidence interval =1.6449,obtained using function =-NORM.S.INV(0.05)

Confidence interval =Mean Standard deviation*critical value/sqrt(sample size)

=197

b.With the hiring of new security guard the amount should fall by $197-$106 = $91

Now,P(X<91) = (Using the normal z-table)