Question

1) Mary is a waitress at Seventh Heaven Burgers. She wants to estimate the mean amount each group at a table leaves a tip. A random sample of 42 tables had a mean of = $7.30. Based on long term experience, σ is known to be about $2.92. Round final answers to nearest cent.

a. Find a 90% confidence interval for the average amount left by all groups.

b. Use part a to estimate an interval of dollar values for Mary’s total tips for a shift with 42 tables.

Answer 1

a)

Given that

mean =7.3

n= 42

σ = 2.92

(1- )* 100 = 90

90% confidence interval is

where

is the value of standard normal variate such that P ( < Z < ) = 1- ,

=  

= (6.5588 , 8.0411)

b) estimate of an interval of dollar values for Mary’s total tips for a shift with 42 tables is 42*6.5588, 42*8.0411)

=( $275.47,$337.73)