Question
In: Statistics and Probability
Each of the following three datasets represent IQ Scores for three random samples of different sizes....
Each of the following three datasets represent IQ Scores for three random samples of different sizes. The population mean is 100 population standard deviation is 15. Compute the sample mean, median and standard deviation for each sample size:
10) Using the sample size of 30 above in problem eight, your child was tested and has an IQ Score of 140. Calculate Z-Scores to answer these questions:
a. If your child has an IQ Score of 75, what percentage of the population has a lower score?
b. What percentage of the population has a IQ Score between 70 and 130?
c. If your child has an IQ Score of 140, what percentage of the population has a higher score?
Solutions
Expert Solution
Solution:
Given that ,
= 100
= 15
A sample of size n = 30 is taken from this population.
Let
be the mean of sample.
The sampling distribution of the
is approximately normal with
Mean
=
= 100
SD
=
= 15 /
30
= 2.7386
a) Find P(
< 75 )
= P[(
-
)/
< (75 -
)/
]
= P[Z < (75 - 100 )/ 2.7386]
= P[Z < -9.13]
z
score = -9.13
b) Find P(70 <
< 130)
= P(
< 130) - P(
< 70)
= P[(
-
)/
< (130 - 100)/2.7386] - P[(
-
)/
< (70 - 100)/2.7386]
= P[Z < 10.95] - P[Z < -10.95]
z
score = 10.95,-10.95
c) Find
P(
> 140 )
= P[(
-
)/
> (140 -
)/
]
= P[ (
-
)/
> (140 - 100 )/02.7386 ]
= P[Z > 14.61 ]
= 1 - P[Z < 14.61 ]
z
score = 14.61
orchestra answered 1 year agoRelated Solutions
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