Question

9. Stan’s Deli is situated inside a large industrial park. The weekday gross sales at Stan’s average $1,240, with a standard deviation of $180. Find the probability that the average over the next 40 weekdays will exceed $1,200. Please note the assumptions that are used in making the calculation.

Answer 1

0.9792

Explanation:

Data provided in the question:

Average gross sales = $1,240

Standard deviation = $180

sample size = 40

Now,

standard deviation of sample average

=
`\frac{\textup{Standard deviation}}{√(n)}`

=
`(180)/(√(40))`

= 28.46

Now,

z value for 1200 =
`((1200-1240))/(28.46)` = -1.4,

and,

p value for (z = -1.4) = 0.0808

therefore,

P(average < $1200) = 0.0808

Thus,

probability that the average over the next 40 weekdays will exceed $1,200

= 1 - 0.808

= 0.9792