Question

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 22 minutes and a standard deviation of 4 minutes. Using the empirical rule, determine the interval of minutes that the middle 68% of customers have to wait.

Answer 1

The middle 60% of the customers have to wait 18 to 26 minutes until their food is served.

Explanation:

Solution:-

- Define a random variable X: The waiting time for any customer at a particular restaurant to be normally distributed with the following analytical parameters.

X ~ Norm ( u , s^2 )

Where,

u: The mean waiting time

s: The standard deviation for the waiting time about mean time.

- The parameters for the random variable are given as such:

X ~ Norm ( 22 , 4^2 ) mins

- The general empirical rule of statistics gives us the probability for normally distributed random variable within one, two and three standard deviations about the mean ( u ):

- The empirical rule says:

P ( u - s < X < u + s ) = 0.68

P ( u - 2*s < X < u + 2*s ) = 0.95

P ( u - 3*s < X < u + 3*s ) = 0.997

- The interval for the middle 60% of the customer are to wait for their order is given by the following range:

P ( u - s < X < u + s ) = 0.68 ( 68% )

Where,

Range for 68% : u - s < X < u + s

Range for 68% : 22 - 4 < X < 22 + 4

Answer:

Range for 68% : (18 < X < 26) mins