Transcript No, he scored 2.78 SD below the mean

Suppose you take the SAT test and the
ACT test. Not using the chart they
provide, can you directly compare your
SAT Math score to your ACT math score?
Why or why not?
We need to standardized these scores so
that we can compare them.
z score
• Standardized score
• Has m = 0 & s = 1
z 
x  mx
sx
Let’s explore . . .So what does the z-score
tell you?
Suppose the mean and standard deviation of a
distribution are m = 50 & s = 5.
If the x-value is 55, what is the z-score?
1
If the x-value is 45, what is the z-score?
-1
If the x-value is 60, what is the z-score?
2
What do these z scores mean?
-2.3
1.8
6.1
-4.3
2.3 s below the mean
1.8 s above the mean
6.1 s above the mean
4.3 s below the mean
Jonathan wants to work at Utopia
Landfill. He must take a test to see if
he is qualified for the job. The test
has a normal distribution with m = 45
and s = 3.6. In order to qualify for the
job, a person can not score lower than
2.5 standard deviations (z score)
below the mean. Jonathan scores 35
on this test. Does he get the job?
No, he scored 2.78 SD below the mean
Sally is taking two different math
achievement tests with different means
and standard deviations. The mean score
on test A was 56 with a standard deviation
of 3.5, while the mean score on test B was
65 with a standard deviation of 2.8. Sally
scored a 62 on test A and a 69 on test B.
On which test did Sally score the best?
She did better on test A.