Question

How do we find a proportion of a population with only a mean and standard deviation?

SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. For each of the SAT scores below, determine what proportion of the population lies below that score.

scores, 550, 640,720,370

Answer 1

Solution:-

Mean = 500, S.D = 100

a) The proportion of the population lies below 550 is 0.6915.

x = 550

By applying normal distribution:-

z = 0.50

Use the z-score table or p-value calculator.

P(z < 0.50) = 0.6915

b) The proportion of the population lies below 640 is 0.9192.

x = 640

By applying normal distribution:-

z = 1.40

Use the z-score table or p-value calculator.

P(z < 1.40) = 0.9192

c) The proportion of the population lies below 720 is 0.9861.

x = 720

By applying normal distribution:-

z = 2.20

Use the z-score table or p-value calculator.

P(z < 2.20) = 0.9861

d) The proportion of the population lies below 370 is 0.0968.

x = 370

By applying normal distribution:-

z = - 1.30

Use the z-score table or p-value calculator.

P(z < - 1.30) = 0.0968