Chapter 8 Review Olympics
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Transcript Chapter 8 Review Olympics
Advanced Math Topics
Chapter 8 Review Olympics
• One sheet per player
• Make an answer column on the left hand side
of your sheet
• Work together to solve each question
• Winning team earns a reward
• We will go over the process and answers for
each
BRONZE
1 point
1) There are 35 students in a math class. The teacher has
assigned each student a number from 1-35. He wants to
randomly select 5 students to answer questions in class.
Use column 1 in the back of the book to select the five
students.
2) 80 computers from each of six different companies have been
tested by Consumer Reports. The average life for each sample
was 14, 28, 11, 13, 9, and 19 months. Find the overall average
of these sample means. Round to the nearest hundredth.
SILVER
2 points
3) 200 bagels from each of five different companies have been
tested to see how many days they will stay good. The average
life for each sample was 9, 18, 13, 12, and 23 days.
Find the standard deviation of the sample means.
Round to the nearest ten-thousandth.
4) The average height of all the workers in a hospital is known
to be 65 inches with a standard deviation of 2.3 inches. If
a sample of 36 people is selected at random, what is the
probability that the average height of these 36 people will be
between 64 and 65.5 inches? Round your answer to the nearest
hundredth of a %.
5) A survey found that the average amount of money spent per
year by a person on auto repairs is $921 with a standard deviation
of $102. If a sample of 49 people is randomly selected, what is
the probability that they spend an average of at most $900 per
year on auto repairs. Round your answer to the nearest
hundredth of a %.
6) The average amount of money that investors have in a
TD-Ameritrade account is $5,000 with a standard deviation of
$650. A random sample of 36 accounts is taken. What is the
probability that the average amount of the accounts is between
$5,200 and $5,300? Round your answer to the nearest
hundredth of a %.
7) The average life of horses is 23 years with a standard deviation
of 2.9 years. A farm has 36 horses. Find the probability that the
average life of the horses on the farm will be more than 22 years.
Round your answer to the nearest hundredth of a %.
GOLD
3 points
8) The number of students who made it to the Wall of Fame
In each of the first five months was 9, 18, 13, 12, and 23. Find
all combinations of sample size 2 and find the standard deviation.
Round your answer to the nearest ten-thousandth.
9) The average life of a projector bulb is 200 hours with a
standard deviation of 11.2 hours. Numerous random samples of
49 bulbs are selected. Within what limits will the middle 95% of
the sample means lie? Round each to the nearest hundredth.
10) The average life of a projector bulb is 200 hours with a
standard deviation of 11.2 hours. Numerous random samples of
49 bulbs are selected. What length bulb will cut off the top 10% of
the sample means? Round to the nearest hundredth.
• Rows 1 and 2 Trade Papers
• Rows 3 and 4 Trade Papers
• Rows 5 and 6 Trade Papers
• Score only one sheet, then add it to their
teammate’s score.
• Points: Gold = 3 Silver = 2 Bronze = 1
• If there is more than 1 part, all parts must be
correct to get the points
BRONZE
1 point
1) There are 35 students in a math class. The teacher has
assigned each student a number from 1-35. He wants to
randomly select 5 students to answer questions in class.
Use column 1 in the back of the book to select the five
students.
Process: Look at the first two digits in the column.
Select any number that is 35 or less.
Answer: Student #’s 10, 22, 24, 28 and 09.
2) 80 computers from each of six different companies have been
tested by Consumer Reports. The average life for each sample
was 14, 28, 11, 13, 9, and 19 months. Find the overall average
of these sample means. Round to the nearest hundredth.
Process: Add them up and divide by the number
of samples.
Answer: 15.67 months
SILVER
2 points
3) 200 bagels from each of five different companies have been
tested to see how many days they will stay good. The average
life for each sample was 9, 18, 13, 12, and 23 days.
Find the standard deviation of the sample means.
Round to the nearest ten-thousandth.
Process: Find the mean of the means(15), subtract this from
each sample mean. Square each difference. Add these
up. Divide by the number of samples (5) and square
root the result.
Answer: 4.9396
4) The average height of all the workers in a hospital is known
to be 65 inches with a standard deviation of 2.3 inches. If
a sample of 36 people is selected at random, what is the
probability that the average height of these 36 people will be
between 64 and 65.5 inches? Round your answer to the nearest
hundredth of a %.
(x ) y
z
Process: Find the z-score for 64 inches (z = -2.61) using the
formula. Find the z-score for 65 inches (z = 1.30) using the
formula. Look these numbers up in the columns in
the chart and add the two probabilities(0.4955 + 0.4032).
Answer: 89.87%
5) A survey found that the average amount of money spent per
year by a person on auto repairs is $921 with a standard deviation
of $102. If a sample of 49 people is randomly selected, what is
the probability that they spend an average of at most $900 per
year on auto repairs. Round your answer to the nearest
hundredth of a %.
(x ) y
z
Process: Find the z-score for $900 (z = -1.44) using the
formula. Look this up in the columns in the chart(0.4251).
Drawing the bell curve and shading to the LEFT will make
it apparent to SUBTRACT 0.4251 from 0.5000.
Answer: 7.49%
6) The average amount of money that investors have in a
TD-Ameritrade account is $5,000 with a standard deviation of
$650. A random sample of 36 accounts is taken. What is the
probability that the average amount of the accounts is between
$5,200 and $5,300? Round your answer to the nearest
hundredth of a %.
(x ) y
z
Process: Find the z-score for $5200 (z = 1.85) using the
formula. Find the z-score for $5300 (z = 2.77) using the
formula. Look these up these numbers in the columns in
the chart and SUBTRACT the two probabilities(0.4972 - 0.4678)
because they are both to the right of the mean.
Answer: 2.94%
7) The average life of horses is 23 years with a standard deviation
of 2.9 years. A farm has 36 horses. Find the probability that the
average life of the horses on the farm will be more than 22 years.
Round your answer to the nearest hundredth of a %.
z
(x ) y
Process: Find the z-score for 22 years (z = -2.07) using the
formula. Look this up in the columns in the chart and
ADD this to 0.5000 because 22 is to the left of the mean and the
shading is to the right. 0.5000 + 0.4808
Answer: 98.08%
GOLD
3 points
8) The number of students who made it to the Wall of Fame
In each of the first five months was 9, 18, 13, 12, and 23. Find
all combinations of sample size 2 and find the standard deviation.
Round your answer to the nearest ten-thousandth.
Process: Create all possible sample combinations, there are 10.
Find the sample mean for each sample. Find the average of the
sample means. Subtract this from each sample mean. Square
each difference. Add them up, divide by the number of samples,
and take the square root.
Answer: 3.0249
9) The average life of a projector bulb is 200 hours with a
standard deviation of 11.2 hours. Numerous random samples of
49 bulbs are selected. Within what limits will the middle 95% of
the sample means lie? Round each to the nearest hundredth.
Process: Since you are solving for x bar, use the formula.
Fill in all known values. To find the z-scores, divide .95 by 2 to
get .4750 and look this up IN the chart (z = 1.96 and z = -1.96).
Plug these in and solve.
Answer: Between 196.86 and 203.14 hours.
xz
x
10) The average life of a projector bulb is 200 hours with a
standard deviation of 11.2 hours. Numerous random samples of
49 bulbs are selected. What length bulb will cut off the top 10% of
the sample means? Round to the nearest hundredth.
Process: Since you are solving for x bar, use the formula.
Fill in all known values. To find the z-score, look up 0.4 IN the
chart (z = 1.28). Plug this in and solve.
xz
Answer: 202.05 hours.
x
Tiebreaker) You took many samples of 50 people and wrote down
their height. You found that the average height was 5’ 8’’ with a
standard deviation of 2.4767 inches. Your friend took many
samples of size 100 from the same population. He found the
average to be the same as yours but had a different standard
deviation. Which of these could be his standard deviation?
2.3, 2.4767, or 2.5 inches.
Answer:
2.3
HW
• P. 432 #1-6, 9
• To study, look at this slideshow, past
slideshows, the book, the chapter review,
etc.
• Winners: Odds
• Test is on Wednesday