Answer:
(a) 45.4%
(b) 591
Step-by-step explanation:
(a) μ = 19.6, σ = 5.2
First, find the z-score.
z = (x − μ) / σ
z = (19 − 19.6) / 5.2
z = -0.115
Use a chart or calculator to find the probability.
P(Z < -0.115) = 0.454
45.4% of the scores are less than 19.
(b) First, find the z-score.
z = (x − μ) / σ
z = (21 − 19.6) / 5.2
z = 0.269
Use a chart or calculator to find the probability.
P(Z > 0.269) = 1 − P(Z < 0.269)
P(Z > 0.269) = 1 − 0.606
P(Z > 0.269) = 0.394
39.4% of the scores are greater than 21. There are 1500 scores, so 39.4% of that is 591.
