MATH 225N WEEK 5(STATISTICS) 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.
Rounding to the nearest integer, x1≈78. The probability to the left of x2 is
0.25+0.50=0.75. Use Excel to find x2.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.75,81,4) and press
ENTER.
Rounding to the nearest integer, x2≈84. Thus, the middle 50% of the exam scores
are between 78 and 84.
5. The number of walnuts in a mass-produced bag is modeled by a normal
distribution with a mean of 44 and a standard deviation of 5. Find the number of
walnuts in a bag that has more walnuts than 80% of the other bags.
Use Excel, and round your answer to the nearest integer. 48
Here, the mean, μ, is 44 and the standard deviation, σ, is 5. Let x be the number of
walnuts in the bag. The area to the left of x is 80%=0.80. Use Excel to find x.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.80,44,5) and press
ENTER.
The answer, rounded to the nearest integer, is x≈48. Thus, there are 48 walnuts in a
bag that has more walnuts than 80% of the other bags.
6. A firm’s marketing manager believes that total sales for next year will follow the
normal distribution, with a mean of $3.2 million and a standard deviation of
$250,000. Determine the sales level that has only a 3% chance of being exceeded
next year.
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.
Rounding to the nearest integer, x1≈78. The probability to the left of x2 is
0.25+0.50=0.75. Use Excel to find x2.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.75,81,4) and press
ENTER.
Rounding to the nearest integer, x2≈84. Thus, the middle 50% of the exam scores
are between 78 and 84.
5. The number of walnuts in a mass-produced bag is modeled by a normal
distribution with a mean of 44 and a standard deviation of 5. Find the number of
walnuts in a bag that has more walnuts than 80% of the other bags.
Use Excel, and round your answer to the nearest integer. 48
Here, the mean, μ, is 44 and the standard deviation, σ, is 5. Let x be the number of
walnuts in the bag. The area to the left of x is 80%=0.80. Use Excel to find x.
1. Open Excel. Click on an empty cell. Type =NORM.INV(0.80,44,5) and press
ENTER.
The answer, rounded to the nearest integer, is x≈48. Thus, there are 48 walnuts in a
bag that has more walnuts than 80% of the other bags.
6. A firm’s marketing manager believes that total sales for next year will follow the
normal distribution, with a mean of $3.2 million and a standard deviation of
$250,000. Determine the sales level that has only a 3% chance of being exceeded
next year.
