Question

The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3. You take water specimens from 4 randomly selected locations on this river basin.

1. What is the probability that the mean pH measurement of these 4 specimens is greater than 8.2?
A. 0.2546
B. 0.7454
C. 0.0918
D. 0.9082

Answer 1

C) 0.0918

Explanation:

Let
`\bar{X}` be the mean pH measurement of these 4 specimens, we know that this random variable is normally distributed with mean 8 and standard deviation
`0.3/√(4)=0.3/2=0.15`, this because we have a sample size n = 4. We are looking for
`P(\bar{X}>8.2)`, the z-score related to 8.2 is (8.2-8)/0.15=1.3333, therefore,
`P(\bar{X}>8.2) = P(Z > 1.3333) = 0.0912`.