Question

Suppose the grade on a Math test is normally distributed with mean 78 and standard deviation 10.

(c) Rob achieved a grade that exceeded 95% of all grades. Find Rob’s actual grade.

(d) Suppose 32% of students did better than Mei. Find Mei’s actual grade.

Please explain the z=score/z=table process

Answer 1

Solution:

Given that,

mean = = 78

standard deviation = = 10

c)

P(Z > z ) = 95%

1 - P(Z < z ) = 0.95

P(Z < z ) = 1 - 0.95

P(Z < z ) = 0.05

P(Z < -1.65) = 0.05

z = -1.65

Using z-score formula,

X = z* +

= -1.65 * 10 + 78

= 61.5

Rob’s actual grade is 61.5

d)

P(Z > z ) = 32%

1 - P(Z < z ) = 0.32

P(Z < z ) = 1 - 0.32

P(Z < z ) = 0.68

P(Z < 0.47) = 0.68

z = 0.47

Using z-score formula,

X = z* +

= 0.47 * 10 + 78

= 82.7

Mei’s actual grade is 82.7