Question

The manager of a local diner has calculated his average daily sales to be $4500 within a standard deviation of $750.

a. In what range can the manager expect his daily sales to be 68% of the time?

b. In what range can the manager expect his daily sales to be 95% of the time?

c. In what range can the manager expect his daily sales to be 99.7% of the time?

I have the answer key but do not know how to solve for them. KEY a) $3750 to $5250, b) $3000 to $6000, and c) $2250 to $6750

Answer 1

Ans:

Given that

mean=4500

standard deviation=750

68–95–99.7 rule:68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

a)68% of the daily sales lies witin one standard deviation of the mean i.e.

4500-750=3750

4500+750=5250

b)

95% of the daily sales lies witin two standard deviations of the mean i.e.

4500-2*750=4500-1500=3000

4500+2*750=4500+1500=6000

c)

99.7% of the daily sales lies witin three standard deviations of the mean i.e.

4500-3*750=2250

4500+3*750=6750