The temperature control unit on a commercial freezer in a 24-hour grocery store

Question

The temperature control unit on a commercial freezer in a 24-hour grocery store is set to maintain a mean temperature of 24oF. 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 2.5oF. The desired range is 18oF to 30oF. 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? Please show all Excel functions used.

Explanation / Answer

here mean =24

and std deviation z=2.5

for zscore =(X-mean)/std deviation

hence P(18<X<30)= P((18-24)/2.5<Z<(30-24)/2.5) =P(-2.4<Z<2.4)=normsdist(2.4)-normsdist(-2.4)

=0.9918-0.0082 =0.9836

hence probabilty that  freezer temperature will be out of range =1-0.9836=0.0164

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