Question

Hungry Howies, a local pizza delivery chain, wants to provide the best service possible for its customers. They decide to record the delivery times 100 randomly selected days, taking the average each day. The resulting distribution is approximately normally with an overall mean of 31.2 minutes.

(a) On one randomly selected day the average delivery time was 34 minutes, which is 0.43 standard deviations above the mean. What is the standard deviation of the distribution?

Answer 1

6.5 minutes

Step-by-step explanation:

We solve this question using this z-score formula.

z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = standard deviations above the mean = 0.43

x = 34 minutes

μ = 31.2 minutes

σ = unknown

n = 100

0.43 = (34 - 31.2)/ σ

0.43 = 2.8 / σ

Cross Multiply

0.43 × σ = 2.8

σ = 2.8/0.43

σ = 6.511627907

The standard deviation of the distribution is approximately 6.5 minutes