Question

at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. which of the following is closest to the proportion of orders that are processed in less than 240 seconds? a 0.17 b 0.25 c 0.36 d 0.83

Explanation:

Step1: Calculate the z-score

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x = 240$, $\mu=276$, and $\sigma = 38$.
Substitute the values into the formula: $z=\frac{240 - 276}{38}=\frac{- 36}{38}\approx - 0.95$

Step2: Find the proportion using z - table

We need to find $P(Z < - 0.95)$. Looking up the z - score of - 0.95 in the standard normal distribution table (or using a calculator with normal distribution functionality), the area to the left of $z=-0.95$ is approximately 0.1711, which is closest to 0.17.

Answer:

A. 0.17