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Home Q & A Board Science-Related Homework Help Mathematics Statistics and Probability
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durocksrock durocksrock
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2 years ago
 The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 121 and a standard deviation of 51, but does not necessarily follow a normal distribution.

The probability that a daily average over a given month is greater than x_bar is 2.5%. Calculate x_bar. Give your answer to 3 decimal places.
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#1
Educator
2 years ago
See if this helps:

X ~ N ( µ = 121 , σ = 57 )
P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.025 = 0.975

Looking for the probability 0.975 in standard normal table to calculate critical value Z = 1.96

Z = ( X - µ ) / σ
1.96 = ( X - 121 ) / 57
X = 232.720
P ( X > 232.720 ) = 0.025
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