Question

From past results, a professor knows that the test score of a student taking her final examination is a random variable with mean 65 and a variance known to be 15. What is the probability that a student will score between 50 and 80? (7-8.1.2)

(A) Somewhere between 0.75 and 0.85
(B) Exactly 0.6826
(C) Exactly 0.9333
(D) Somewhere between 0.55 and 0.75

Answer 1

option B

Explanation:

Given,

mean result (μ) = 65

standard deviation (σ)= 15

probability that student will score between 50 and 80

=
`P(50< x <80 )= P[(50-65)/(15) < (x-\mu)/(\sigma) / \sigma < (80-65)/(15)]`

=
`P(50< x <80 )= P[(-15)/(15) < z / \sigma < (15)/(15)]`

=
`P(50< x <80 )= P[-1< z / \sigma <1]`

= P(Z < 1) - P(Z < -1)

Using z table,

= 0.8413 - 0.1587

= 0.6826

the correct answer is option B