Question

During a dinner rush at a local restaurant, a customer left a tip of more than $25, with a standard deviation of $4.

(a) What is the probability that randomly chosen customer left a tip of more than $28?

(b) A waitress had 30 customers during her dinner shift? What is the probability that her average tip was more than $28?

Answer 1

a)

P( X > 28 )

Z = ( X - u ) /s

u= Mean = 25

s = standard deviation = 4

Z = ( 28 -25)/4

= 0.75

P( Z > 0.75) = 0.2266

(b)

P( X > 28 ) and n =30

Z = ( X - u ) /(s/)

Z =  ( 28 -25)/(4/ )

= 4.108

P( Z > 4.108 ) = 0