At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately no

Question

2 months ago

14

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately no

rmal 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?
А
0.17
B
0.25
0.36
D
083
E
0.95

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-02-18T18:01:04+03:00

Answer:

The correct answer is;

A. 0.17

Step-by-step explanation:

Here are the provided details;

The average time taken for a cashier to handle an order, μ = 276 seconds

The deviation from the average, σ = 38 seconds

The z-score for an order processing time of x = 240 seconds can be calculated as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Thus;

$Z=\dfrac{240-276 }{38 } \approx -0.9474$

The resulting probability

P(z = -0.9474) = 0.17361

Hence, the estimated proportion of orders processed in under 240 seconds is roughly 0.17361 or 0.17 when rounded to two decimal places.