MATH 225N, Week 5 Quiz
, MATH 225N, Week 5 Quiz
1. An organization has members who possess IQs in the top 4% of the population. If IQs are
normally distributed, with a mean of 100 and a standard deviation of 15, what is the minimum
IQ required for admission into the organization?
Use Excel, and round your answer to the nearest integer: 126
2. The top 5% of applicants on a test will receive a scholarship. If the test scores are normally
distributed with a mean of 600 and a standard distribution of 85, how low can an applicant
score to still qualify for a scholarship?
Use Excel, and round your answer to the nearest integer. 740
-Here, the mean, μ, is 600 and the standard deviation, σ, is 85. Let x be the score on the test. As the top
5% of the applicants will receive a scholarship, the area to the right of x is 5%=0.05. So the area to the
left of x is 1−0.05=0.95. Use Excel to find x.
-Open Excel. Click on an empty cell. Type =NORM.INV(0.95,600,85) and press ENTER.
-The answer rounded to the nearest integer, is x≈740. Thus, an applicant can score a 740 and still be in
the top 5% of applicants on a test in order to receive a scholarship.
3. The weights of oranges are normally distributed with a mean of 12.4 pounds and a standard deviation
of 3 pounds. Find the minimum value that would be included in the top 5% of orange weights.
Use Excel, and round your answer to one decimal place. 17.3
-Here, the mean, μ, is 12.4 and the standard deviation, σ, is 3. Let x be the minimum value that would be
included in the top 5% of orange weights. The area to the right of x is 5%=0.05. So, the area to the left of
x is 1−0.05=0.95. Use Excel to find x.
-1. Open Excel. Click on an empty cell. Type =NORM.INV(0.95,12.4,3) and press ENTER.
-The answer, rounded to one decimal place, is x≈17.3. Thus, the minimum value that would be included
in the top 5% of orange weights is 17.3 pounds
4. Two thousand students took an exam. The scores on the exam have an approximate normal
distribution with a mean of μ=81 points and a standard deviation of σ=4 points. The middle 50% of the
exam scores are between what two values?
Use Excel, and round your answers to the nearest integer. 78, 84
The probability to the left of x1 is 0.25. Use Excel to find x1.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.25,81,4) and press ENTER.
, MATH 225N, Week 5 Quiz
1. An organization has members who possess IQs in the top 4% of the population. If IQs are
normally distributed, with a mean of 100 and a standard deviation of 15, what is the minimum
IQ required for admission into the organization?
Use Excel, and round your answer to the nearest integer: 126
2. The top 5% of applicants on a test will receive a scholarship. If the test scores are normally
distributed with a mean of 600 and a standard distribution of 85, how low can an applicant
score to still qualify for a scholarship?
Use Excel, and round your answer to the nearest integer. 740
-Here, the mean, μ, is 600 and the standard deviation, σ, is 85. Let x be the score on the test. As the top
5% of the applicants will receive a scholarship, the area to the right of x is 5%=0.05. So the area to the
left of x is 1−0.05=0.95. Use Excel to find x.
-Open Excel. Click on an empty cell. Type =NORM.INV(0.95,600,85) and press ENTER.
-The answer rounded to the nearest integer, is x≈740. Thus, an applicant can score a 740 and still be in
the top 5% of applicants on a test in order to receive a scholarship.
3. The weights of oranges are normally distributed with a mean of 12.4 pounds and a standard deviation
of 3 pounds. Find the minimum value that would be included in the top 5% of orange weights.
Use Excel, and round your answer to one decimal place. 17.3
-Here, the mean, μ, is 12.4 and the standard deviation, σ, is 3. Let x be the minimum value that would be
included in the top 5% of orange weights. The area to the right of x is 5%=0.05. So, the area to the left of
x is 1−0.05=0.95. Use Excel to find x.
-1. Open Excel. Click on an empty cell. Type =NORM.INV(0.95,12.4,3) and press ENTER.
-The answer, rounded to one decimal place, is x≈17.3. Thus, the minimum value that would be included
in the top 5% of orange weights is 17.3 pounds
4. Two thousand students took an exam. The scores on the exam have an approximate normal
distribution with a mean of μ=81 points and a standard deviation of σ=4 points. The middle 50% of the
exam scores are between what two values?
Use Excel, and round your answers to the nearest integer. 78, 84
The probability to the left of x1 is 0.25. Use Excel to find x1.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.25,81,4) and press ENTER.
