Question

Sale amounts during lunch hour at a local subway are normally distributed, with a mean $ 8.21, and a standard deviation of $ 1.26.

a. Find the probability that a randomly selected sale was at least $ 12.74?

b. A particular sale was $ 5.86. What is the percentile rank for this sale amount?

c. Give the sale amount that is the cutoff for the highest 95 %?

d.What is the probability that a randomly selected sale is between $5.00 and $9.00?

e. What sale amount represents the cutoff for the middle 36 percent of sales?

Answer 1

Let X ~ Normal ( )

a) Here we want to find P( X >= 12.74) = 1 - P( X < 12.74) .......( 1 )

Let's use excel:

P( X < 12.74) = "=NORMDIST(12.74,8.21,1.26,1)" = 0.999838

Plug this in equation ( 1 ), we get:

P( X >= 12.74) = 1 - 0.999838 = 0.000162

b) Let's find P( X < 5.86 ) = "=NORMDIST(5.86,8.21,1.26,1)" = 0.0310 = 3.1%

So percentile rank is 3

c) Here we want to find x score such that P( X < x) = 0.95

Let's use excel:

x = "=NORMINV(0.95,8.21,1.26)" = 10.28

d) P( 5 < X < 9 ) = P( X < 9) - P( X < 5) = "=NORMDIST(9,8.21,1.26,1) - NORMDIST(5,8.21,1.26,1" = 0.7292