School has a general aptitude test. The scores on this test are normally distrib

Question

School has a general aptitude test. The scores on this test are normally distributed with mean 115 and standard deviation 11.
a) What percent of the scores on this test are 100 or higher?
b) What percentage of the scores are between 100 and 110?
c) What percentage of the scores are 125 or higher?
d) What percentage of the scores are between 110 and 125?
e) What percentage of the scores are between 120 and 125?
f) What percentage of the scores are lower than 110?
g) What percentage of the scores are lower than 130?

Explanation / Answer

Mean = 115 and S.D. = 11

Z is a standard normal deviate, then Z = (X )/ will have a standard normal distribution.

Using standard noraml distribution curve :

a) X >= 100 i.e

. P(Z > -15/11) = 91.37 %

b) between 100 and 110

P(-15/11 <Z< -5/11) = 24%

c) x > = 125

i.e.P( z >= 10/11 ) = 18.17%

d) 110 < X < 125

P(-5/11 < Z < 10/11 ) = 49.36%

e) 120 <X < 125

P(5/11 < Z < 10/11) = 14.31%

f) X< 110

P(Z<-5/11) = 32.47%

g) X <130

ie. P(Z < 15/11) = 91.37%

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