Normal Distribution Problem

Mar 2017
3
0
USA
The temperature control unit on a commercial freezer in a 24-hour grocery store is set to maintain a mean temperature of 24 F. The temperature varies because people are constantly opening the freezer to remove items, but the thermostat is capable of maintaining temperature with a standard deviation of 2.5F. The desired range is 18F to 30F. You can assume that freezer temperature is normally distributed.

i. Assuming that the temperature control unit is working properly, what is the
probability that the freezer temperature will be out of range at any point in time?

ii. In order to ensure that the control unit is working properly, the store samples the
freezer temperature 4 times every 24 hours – at midnight, 6AM, 12 noon and 6PM.
If the average of these four values falls outside a range {LL, UL} then the store
concludes that the control unit is not working properly and shuts the freezer down
for costly inspection and repairs. What values would you choose for LL and UL
such that there is only a 1% chance of your shutting down the machine when in fact
it is working properly?
 

romsek

MHF Helper
Nov 2013
6,671
3,005
California
would be happy to help you with any specific problems but you need to show some work for this.