In: Statistics and Probability
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
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