Question

The average clothes washer uses 15 gallons of water per load, with a standard deviation of 3.0 gallons. What is the probability that a random sample of 90 loads will provide a sample mean within one half gallon of the population mean

Answer 1

0.866

Explanation:

Given that:

Mean gallon (m) = 15

Standard deviation (σ) = 3

Sample size (n) = 90

Using the relation :

Zscore = (x - m) / (σ/√n)

The zscore being within 1.5 of population mean

-1.5 < z < 1.5

From z distribution table :

0.93319 - 0.0668

= 0.866