Question

In: Statistics and Probability

Each of the following three datasets represent IQ Scores for three random samples of different sizes....

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 ago

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