Question

Suppose the amount of time customers have to wait for their order at a coffee shop has an approximate normal distribution with a mean of 112 seconds and a standard deviation of 17.2 seconds. If the wait time for a customer is 101 seconds, what is the z-score? Express the answer as a decimal value rounded to the nearest thousandth (three digits to the right of the decimal point).

Answer 1

The z-score of a customer's wait time at the coffee shop of 101 seconds, with a mean of 112 seconds and a standard deviation of 17.2 seconds, is approximately -0.640.

Step-by-step explanation:

To calculate the z-score for the given wait time at the coffee shop, we use the formula z = (X - μ) / σ, where X is the wait time for a customer, μ is the mean wait time, and σ is the standard deviation of the wait times. Substituting the given values, we get:

z = (101 seconds - 112 seconds) / 17.2 seconds
z = -11 / 17.2
z ≈ -0.640

Rounded to the nearest thousandth, the z-score for a wait time of 101 seconds is -0.640.