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.

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

Step-by-step 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