Question

Consider a test whose scores have a normal​ distribution, a mean of 104​, and a standard deviation of 16. Find the lowest score a person would need to be in each of the following top percentages. ​(a) 2​% ​(b) 5​% Click here to view page 1 of the Normal Curve Areas. LOADING... Click here to view page 2 of the Normal Curve Areas. LOADING... Click here to view page 3 of the Normal Curve Areas. LOADING... Click here to view page 4 of the Normal Curve Areas. LOADING... ​(a) The lowest score on the test a person can have while being in the top 2​% is

Answer 1

Solution,

Given that,

mean = = 104

standard deviation = = 16

Using standard normal table

a) P(Z > z ) = 2%

= 1 - P(Z < z ) = 0.02

=P(Z < z ) = 1 - 0.02

=P(Z < z ) = 0.98

P(Z < 2.054 ) = 0.98

z = 2.054

Using z-score formula,

x = z * +

x = 2.054 * 16 + 104

x = 136.86

lowest scores = 136.86

Using standard normal table

b) P(Z > z ) = 5%

= 1 - P(Z < z ) = 0.05

=P(Z < z ) = 1 - 0.05

=P(Z < z ) = 0.95

P(Z < 1.645 ) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 16 + 104

x = 130.32

lowest scores = 130.32