Question

Given a variable with the following population parameters: Mean = 20. Variance = 16.

a) What is the probability of obtaining a score greater than 18 and less than 21?

b) What is the score at which 75% of the data falls at or below?

c) What is the score at which 25% of the data falls at or above?

d) Within what two scores do 95% of the scores fall (i.e symmetrically)?

Bold answers.

Answer 1

Mean, = 20.

Variance, = 16.

a) P( 18 < X < 21) = P( < < )

= P( -0.5 < z < 0.25)

= P( z < 0.25 ) - P(z < -0.5)

= P(z < 0.25) -1 + P(z < 0.5)

= 0.59871- 1 + 0.69146

= 0.29017

b) For score at which 75% of the data falls at or below, we need to find the 75th percentile

P( Z <z ) = 0.75

P( Z < 0.674) =0.75 ( from normal z score table)

z = 0.674

=0.674

=0.674

X = 22.696

c) For score at which 25% of the data falls at or above, we need to find the 75th percentile

  score at which 25% of the data falls at or above, X= 22.696 ( calculated above)

d) According to Empirical rule 95% of the data lie within the 2 standard deviation of the mean

So two scores do 95% of the scores fall is ( 20- ) & ( 20+ ) i.e ( 16, 24)