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2. Suppose the temperature that most foods can stay bacteria free in restaurants varies approximately according to a normal distribution with a mean of 31.3 degrees and a standard deviation of 2.8 degrees Fahrenheit. The Federal Department of Agriculture mandates that food inspectors make sure that all restaurants fine a location up to $1,500.00 if the temperature in cold food storage goes above the bottom 15% of that distribution for safety and insurance purposes. What temperature correlates to the bottom 15% of this distribution?

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Answer:

28.4

Step-by-step explanation:

Given that:

Mean, m = 31.3

Standard deviation, s = 2.8

Since, data is normally distributed :

P(x < 0.15) gives a Z value of - 1.036

Using the Zscore formula :

Z = (x - mean) / standard deviation

-1.036 = (x - 31.3) / 2.8

-1.036 * 2.8 = x - 31.3

-2.9008 = x - 31.3

-2.9008 + 31.3 = x

28.3992 = x

The temperature which correlates to the bottom 15% of the distribution is 28.4