Question

You will be asked to calculate either raw scores or percentages. For each question write out your calculation, the appropriate Z score, what on the curve you should be shading, the exact percentage from the normal curve table and the final answer.

A group of students take a Statistics quiz where the average was M = 90 and the standard deviation was SD = 7.8. Answer the following questions regarding this distribution using your normal curve table. Depending on the problem, be sure to identify the raw scores, Z scores, what in particular you shaded when creating a curve and the final answer. (5 pts each)

6.         What percentage of the population lands between the raw scores of 82 and 107?

7.         If you score a 85, what percentage of the population scored above you?

8.         What raw score is needed to be in the bottom 16%?

9.         If you score a 96, what percentage of the population scored above you?

please type out the answer instead of writing it on a piece of paper. thank you so much!

Answer 1

Solution,

Given Data,

M=90 ( mean )

Let X is the Raw score & X is normally distributed.

(6) P( 82 < X < 107 ) =

=P( -1.02564 < X < 2.179487 )

=P ( Z< 2.1795) - P(Z< -1.0256 )

= 0.98535-0.15254

=0.83281

=0.8328

(7) P( X > 85 )

=P( Z > -0.6410256)

=1- P( Z< -0.6410)

=1-0.28076

=0.7392

(8) P ( X < x ) = 0.16 =P ( Z < -0.9945 )

so. x = M+Z*

x= 90-0.9945*7.8

x= 82.2429

(9)

(7) P( X > 96 )

=P( Z > 0.76923)

=1- P( Z< 7692)

=1-0.77912

=0.22087

=0.2209