Question

The test grades in some class follow a normal distribution (we will call it X) with σ = 8. Use this information (and the chart!) to answer the following questions:
(a) If there is a 60% chance that a student scores higher than a 75, find µ, the average test grade for this class.
(b) Using the µ you found in part (a), determine P(72 ≤ X ≤ 90).

Answer 1

Solution :

σ = 8 , X :  test grades in some class

a)

P( x > 75 ) = 0.6000

P ( x < 75 ) = 1-0.6000 = 0.4000

Form Normal distribution table,

z = -0.25

We know that , x = zσ + µ

75 = -0. 25*8 + µ

µ = 75 + 0. 25*8

µ = 77

Answer : µ = 77

b)

P(72 ≤ X ≤ 90) = P((72-µ)/σ≤ z ≤(90-µ)/σ)

= P(-0.63 < z < 1.63)

= 0.94845 - 0.26435

= 0.6841

P(72 ≤ X ≤ 90) = 0.6841