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.
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)
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