Question

9) Peter sells ice cream at a local playground. His average daily income is $180 with a standard deviation of $25. Assume Peter's earnings are normally distributed.

a. Peter made $175 today. Based on his past earnings, what is the z-score for $175? (Round to no less than two decimal places.)  

b. What is the probability that Peter will make $175 or more tomorrow? (Give the proportion correct to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 180

standard deviation = = 25

a

using z score formula

z = (x -) / = (175 - 180) / 25 = -0.2

b

P(x > 175) = 1 - P(x< 175)

= 1 - P[(x -) / < (175 - 180) / 25]

= 1 - P(z <-0.2 )

Using z table

= 1 -  0.4207

probability= 0.5793