5. A population of daily sales figures is approximately normally distributed wit

Question

5.   A population of daily sales figures is approximately normally distributed with a mean of $14,000 and a standard deviation of $3,000.

(a)       You’d like to predict tomorrow’s sales. (Yes, this is an inference question.)   Give an interval (a, b) for which you are willing to say that the probability is about 95% that tomorrow’s sales will be between a and b.

(b)       You’d like to predict the average sales over the next 15 business days. (This is another inference question.) Give an interval (c, d) for which you are will to say that the probability is about 95% that the sales over the next 15 business days will be between c and d.

Explanation / Answer

a) = 3000, µ = 14000

For 95% CI, zcrit = 1.96
Margin of error, ME = zcrit* = 1.96*3000 = 5880
lower bound = µ - ME = 14000-5880 = 8120
upper bound = µ + ME = 14000+5880 = 19880

b) Margin of error, ME = zcrit*/sqrt(n) = 1.96*3000/sqrt(15) = 1518.209
lower bound = µ - ME = 14000-1518.209 = 12481.79
upper bound = µ + ME = 14000+1518.209 = 15518.21

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