Answer to Question #222919 in Statistics and Probability for Mustafa Zaidi

Question #222919

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need a fourth person tomorrow? Include evidence of your work by typing out your solution fully.



1
Expert's answer
2021-08-04T14:40:15-0400

Let X=X= the number of customers: XN(μ,σ2).X\sim N(\mu, \sigma^2).

Given μ=60,σ=15.\mu=60, \sigma=15.


P(X>70)=1P(X70)P(X>70)=1-P(X\leq 70)

=1P(Z70μσ)=1P(Z706015)=1-P(Z\leq \dfrac{70-\mu}{\sigma})=1-P(Z\leq \dfrac{70-60}{15})

=1P(Z0.6667)0.2525=1-P(Z\leq 0.6667)\approx0.2525

The probability that they will need a fourth person tomorrow is 0.2525.



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