Question

On average, it takes a shoe factory 21 minutes, with a standard deviation of 3 minutes, to manufacture a pair of running shoes. How often will it take the factory more than 27 minutes to manufacture a pair of running shoes?

Answer 1

Answer:

The number of times it would take more than 27 minutes to manufacture a pair of running shoes is 2.275 times or approximately 2 times per every 100 shoes

Step-by-step explanation:

The average time it takes to manufacture a pair of shoes = 21 minutes;

The standard deviation = 3 minutes

To find how often it takes more than 27 minutes to manufacture a pair of running shoes, we have;

Standard score, given as follows;

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

Where;

x = The raw score = 27 minutes

μ = The average score = 21 minutes

σ = The standard deviation = 3 minutes

From which we have;

$Z=\dfrac{27-21 }{3 } = 2$

Therefore, it is borderline unusual with a p value of P(z>2) = 1 - 0.97725 = 0.02275

Therefore, the number of times out of 100 that it would take more than 27 minutes to manufacture a pair of running shoes = 100 × 0.02275 = 2.275 times which is approximately 2 times in every 100 shoes.