Question

Final exam scores in a Math class with large number of students have mean 145 and standard deviation 4.1. Provided the scores of this Final exam follow a normal distribution, what's the probability that a student scores below 145 OR above 157.3? Find the answer without using the LSND program. (Write the answer in decimals)

Answer 1

Solution:

Given:  Final examination scores in a Math class   follow a normal distribution with Mean = and a  standard deviation = .

We have to find:

P( X < 145 or X > 157.3) = ...........?

P( X < 145 or X > 157.3) = P( X < 145) + P(X > 157.3)

Find z score for x = 145 and for x = 157.3

Thus we get:

P( X < 145 or X > 157.3) = P( X < 145) + P(X > 157.3)

P( X < 145 or X > 157.3) = P( Z < 0.00) + P(Z > 3.00)

P( X < 145 or X > 157.3) = P( Z < 0.00) + [ 1 - P(Z < 3.00) ]

Look in z table for z = 0.0 and 0.00 as well as for  z = 3.0 and 0.00  and find corresponding area.

P(Z < 3.00 ) = 0.9987

and

P( Z<0.00) = 0.5000

Thus

P( X < 145 or X > 157.3) = P( Z < 0.00) + [ 1 - P(Z < 3.00) ]

P( X < 145 or X > 157.3) = 0.5000  + [ 1 - 0.9987 ]

P( X < 145 or X > 157.3) = 0.5000  + 0.0013

P( X < 145 or X > 157.3) = 0.5013