Question

Scores of high school seniors taking the English Regents examination in New York State are normally distributed with a mean of 70 and a standard deviation of 10.

Required:
a. Find the probability that a randomly selected high school senior will have a score between 70 and 75.
b. Find the probability that a randomly selected high school senior will have a score higher than 85.

Answer 1

0.19146

0.066807

Explanation:

Given that :

Mean (m) = 70

Standard deviation (s) = 10

a. Find the probability that a randomly selected high school senior will have a score between 70 and 75.

X ≤ 70 :

Using : z = (x - m) / s

Z = (70 - 70) / 10

Z = 0 / 10

Z = 0

P( Z < 70) = 0.500

X ≤ 75

z = (x - m) / s

Z = (75 - 70) / 10

Z = 5 / 10

Z = 0. 5

P(z < 0.5) = 0.69146

0.69146 - 0.5000

= 0.19146

b. Find the probability that a randomly selected high school senior will have a score higher than 85.

X ≥ 85

z = (x - m) / s

Z = (85 - 70) / 10

Z = 15 / 10

Z = 1.5

P(z > 1.5) = 0.066807 ( Z probability calculator)