Exam grades Scores on a statistics final in a large class we

Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 80 and a standard deviation of 7. Between what two values is the middle 40% of the scores? Please Explain.

Solution

Given that,scores on a statistics final in a large class were normally distributed with a mean of 80 and a standard deviation of 7.

The middle area of the standard normal curve is 40%.

Therefore, the remaining areas (to the left of -z and to the right of z) is 60%.

Because the normal distribution is symmetric, the area to the left of -z is the same as the area to the right of z , each being 30% or 0.3.

This means the area below z (to the left of z) is 0.70.

First we find score for area is 0.30

that is P(Z <=z) = 0.30

We can find this probability by using EXCEL.

syntax :

=NORMSINV(probability)

where probability = area of the left tail = 0.30

z = -0.5244

and the second score is,

P(- z Z z) = 0.4

P(Z z) - P(Z - z) = 0.4

P(Z z) = 0.4 + 0.3 = 0.7

P(Z <= z) = 0.7

EXCEL syntax is,

=NORMSINV(probability)

where, probability = 0.7

z = 0.5244