In a previous section of PSY230, the second test was worth 100 points. The score

Question

In a previous section of PSY230, the second test was worth 100 points. The scores from that class were normally distributed with a mean ( ) of 75 and a standard deviation () of 10. If the exam scores were converted to a Z distribution, the distribution would form a perfect bell shape. The following questions require locating individual IQ scores on the Z distribution and examine the percentage (or proportion) of cases above or below a score. Toms Score is 70.

a) John obtained a score of 90. What is John’s z score?

b) What is the percentage of the students that scored higher than John?

c) If 60 students were in that class, how many of them scored lower than John’s score?

Explanation / Answer

a. Z = (X - ) /

X=90 and mean, =75
Z = (90 - 75) / 10
Z = 1.5

b. number of students that scored more than john can be obtained by calculating the area between 90 and 100

z score for 90=1.5

z acore for 100=2.5

The area between 1.5 and 2.5 is =.9938-.9332

=.0606

=6% approx

c. percentage of students scoring more than john =(1-.0606)*100=93.34%

if there are 60 students in the class, number of students who scored lowe than john =60*93.34/100=56 students approx

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