Answer:
A) 0.3336; B) 0.8531
Step-by-step explanation:
<u>For part A</u>,
We use the z-score formula for an individual score:
Our X value is 332, our mean, μ, is 335, and our standard deviation, σ, is 7:
z = (332-335)/7 = -3/7 ≈ -0.43
Using a z table, we see that the area under the curve less than this (the probability that X is less than this value) is 0.3336.
For part B,
We use the z-score formula for the mean of a sample:
Our X-bar value is 332, our mean, μ, is 335, our standard deviation, σ, is 7, and our sample size, n, is 6:
z = (332-335)/(7÷√6) = 3/2.8577 ≈ 1.05
Using a z table, we see that the are under the curve to the left of this, or the probability less than this, is 0.8531.