Answer to Question #339786 in Statistics and Probability for Sweet pea

Question

Customers at the restaurant have to wait an average of 25 minutes before they receive their meal from the time their order was placed. Assume these waiting times are normally distributed with a standard deviation of 5 minutes.

3.1) What is the probability that a randomly selected customer waits between 20 and 35 minutes before receiving his meal from the time his order was placed?

3.2) What is the maximum waiting time for a customer to receive her meal if she is in the 10% of customers who receive their meals in the fastest time from when the order was placed?

Answer 1

3.1)

$$P(20<X<35)=P(Z<\dfrac{35-25}{5})$$

$$-P(Z\le\dfrac{20-25}{5})=P(Z<2)-P(Z\le-1)$$

$$\approx0.97725-0.15866\approx0.8186$$

3.2)

$$P(X<x)=P(Z<\dfrac{x-25}{5})=0.10$$

$$\dfrac{x-25}{5}=-1.2816$$

$$x=18.59$$