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 fivestudents.

2) 80 computers from each of six different companies have been tested by Consumer Reports. The average life for each samplewas 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 knownto be 65 inches with a standard deviation of 2.3 inches. Ifa sample of 36 people is selected at random, what is the probability that the average height of these 36 people will bebetween 64 and 65.5 inches? Round your answer to the nearesthundredth of a %.

5) A survey found that the average amount of money spent peryear by a person on auto repairs is $921 with a standard deviationof $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 nearesthundredth 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 nearesthundredth of a %.

7) The average life of horses is 23 years with a standard deviationof 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 FameIn each of the first five months was 9, 18, 13, 12, and 23. Findall 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 fivestudents.

Answer: Student #’s 10, 22, 24, 28 and 09.

Process: Look at the first two digits in the column.Select any number that is 35 or less.

2) 80 computers from each of six different companies have been tested by Consumer Reports. The average life for each samplewas 14, 28, 11, 13, 9, and 19 months. Find the overall average of these sample means. Round to the nearest hundredth.

Answer: 15.67 months

Process: Add them up and divide by the numberof samples.

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.

Answer: 4.9396

Process: Find the mean of the means(15), subtract this fromeach sample mean. Square each difference. Add theseup. Divide by the number of samples (5) and squareroot the result.

4) The average height of all the workers in a hospital is knownto be 65 inches with a standard deviation of 2.3 inches. Ifa sample of 36 people is selected at random, what is the probability that the average height of these 36 people will bebetween 64 and 65.5 inches? Round your answer to the nearesthundredth of a %.

Answer: 89.87%

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 inthe chart and add the two probabilities(0.4955 + 0.4032).

yx

z)(

5) A survey found that the average amount of money spent peryear by a person on auto repairs is $921 with a standard deviationof $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 nearesthundredth of a %.

Answer: 7.49%

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.

yx

z)(

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 nearesthundredth of a %.

Answer: 2.94%

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 inthe chart and SUBTRACT the two probabilities(0.4972 - 0.4678)because they are both to the right of the mean.

yx

z)(

7) The average life of horses is 23 years with a standard deviationof 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 %.

Answer: 98.08%

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 theshading is to the right. 0.5000 + 0.4808

yx

z)(

GOLD

3 points

8) The number of students who made it to the Wall of FameIn each of the first five months was 9, 18, 13, 12, and 23. Findall combinations of sample size 2 and find the standard deviation.Round your answer to the nearest ten-thousandth.

Answer: 3.0249

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. Squareeach difference. Add them up, divide by the number of samples,and take the square root.

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.

Answer: Between 196.86 and 203.14 hours.

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.

xzx

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.

Answer: 202.05 hours.

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.

xzx

Answer: 2.3

Tiebreaker) You took many samples of 50 people and wrote down their height. You found that the average height was 5’ 8’’ with astandard deviation of 2.4767 inches. Your friend took many samples of size 100 from the same population. He found theaverage to be the same as yours but had a different standarddeviation. Which of these could be his standard deviation?2.3, 2.4767, or 2.5 inches.

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