Question 6 Find the z-score for an IQ test score of 125 when the mean is 100 and

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Question 6
Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15. (Round to the nearest decimal number with two decimal places.)

Question 7
A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximately normally distributed with a mean of 25 and a standard deviation of 6. The higher the score the greater the motivation to do well in school. Answer questions 7 to 10.

7. What percentage of students taking this test will have scores below 15? (Round your answer to the closest decimal number with 4 decimal places.)
Question 8
What percentage of students taking this test will have scores between 10 and 20? (Round to the nearest decimal number with 4 decimal places.)

Question 9

What percentage of students taking this test will have scores above 30? (Round to the nearest decimal number with 4 decimal places.)

Question 10
John is told that 30% of the students taking the test have higher motivation scores than he does. What was John's score? (Round to the nearest integer) Question 6
Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15. (Round to the nearest decimal number with two decimal places.)

Question 7
A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximately normally distributed with a mean of 25 and a standard deviation of 6. The higher the score the greater the motivation to do well in school. Answer questions 7 to 10.

7. What percentage of students taking this test will have scores below 15? (Round your answer to the closest decimal number with 4 decimal places.)
Question 8
What percentage of students taking this test will have scores between 10 and 20? (Round to the nearest decimal number with 4 decimal places.)

Question 9

What percentage of students taking this test will have scores above 30? (Round to the nearest decimal number with 4 decimal places.)

Question 10
John is told that 30% of the students taking the test have higher motivation scores than he does. What was John's score? (Round to the nearest integer) Question 6
Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15. (Round to the nearest decimal number with two decimal places.)

Question 7
A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximately normally distributed with a mean of 25 and a standard deviation of 6. The higher the score the greater the motivation to do well in school. Answer questions 7 to 10.

7. What percentage of students taking this test will have scores below 15? (Round your answer to the closest decimal number with 4 decimal places.)
Question 8
What percentage of students taking this test will have scores between 10 and 20? (Round to the nearest decimal number with 4 decimal places.)

Question 9

What percentage of students taking this test will have scores above 30? (Round to the nearest decimal number with 4 decimal places.)

Question 10
John is told that 30% of the students taking the test have higher motivation scores than he does. What was John's score? (Round to the nearest integer)

Explanation / Answer

Question 6

Z-score=(Raw score-Mean)/Standard deviation

=(125-100)/15

=25/15

=1.67

Question 7

Z-score for 15 is Z=(Raw score-Mean)/Standard deviation

=(15-25)/6

=-1.67

So, percentage of students taking this test will have scores below    15

=P(Z<-1.67)

= 0.0475 , using excel function =NORMSDIST(-1.67)

=4.75%

Question 8

Z-score for 10 is Z=(Raw score-Mean)/Standard deviation

=(10-25)/6

=-2.50

So, percentage of students taking this test will have scores below    10

=P(Z<-2.50)

= 0.0062, using excel function =NORMSDIST(-2.50)

Z-score for 20 is Z=(Raw score-Mean)/Standard deviation

=(20-25)/6

=-0.83

So, percentage of students taking this test will have scores below    20

=P(Z<-0.83)

=0.2033, using excel function =NORMSDIST(-0.83)

So, percentage of students taking this test will have scores between 10 and 20

=P(10<X<20)

=P(-2.50<Z<-0.83)

= P(Z<-0.83)-P(Z<-2.50)

=0.2033-0.0062

=0.1971

=19.71%

Question 9

Z-score for 30 is Z=(Raw score-Mean)/Standard deviation

=(30-25)/6

=0.83

So, percentage of students taking this test will have scores below 30

=P(Z<0.83)

= 0.7967, using excel function =NORMSDIST(0.83)

Hence, percentage of students taking this test will have scores above 30

=1-0.7967

=0.2033

=20.33%

Question 10

We have to find x0 such that P(X>x0)=0.30

So, P(X<x0)=1-0.30=0.70

P((X-Mean)/Standard deviation<(x0- Mean)/Standard deviation)=0.70

P(Z<z0)=0.70 , where z0=(x0-Mean)/Standard deviation

We have z0= 0.5244 using excel function =NORMSINV(0.7)

Hence, x0=Mean+0.5244*Standard deviation= 25+0.5244*628

  

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