Advanced Math Topics

Chapter 6 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) Find the missing probability.

x p(x)

0 ?

1 0.23

2 0.08

3 0.04

4 0.44

2) Find the mean of the probability distribution.

x p(x)

0 0.1

1 0.1

2 0.1

3 0.2

4 0.15

5 0.3

6 0.05

3) 45% of college applicants into the UC system are accepted. If there are 200,000applicants, how many can be expected tobe accepted? What is the standard deviation.Round to the nearest hundredth.

4) If the variance of a probability distributionis 3.457, what is the standard deviation?Round to the nearest hundredth.

SILVER

2 points

5) Find the standard deviation to the nearest hundredth.

x p(x)

0 0.11

1 0.21

2 0.4

3 0.12

4 0.10

5 0.04

6 0.02

6) The probability that a customer at a gasstation purchases diesel is 0.15. If six drivers pull into a gas station, find the probability that exactly 2 of them purchase diesel. Round to the nearesthundredth of a percent.

7) The number of particles emitted froma radioactive source has an average of4 particle per minute. Find the probability that exactly 2 are emitted. Round to the nearesthundredth of a percent.

8) A package of mixed nuts contains 20walnuts and 80 almonds. Five are grabbedin one handful. Find the probability that exactly one is a walnut. Round to the nearesthundredth of a percent.

GOLD

3 points

9) Men’s Wearhouse got a shipment of90 suits. Eight of them are missing shoes.You randomly grabbed 6 suits. Find the probability that at least 5 have shoes. Round to the nearesthundredth of a percent.

10) According to police statistics, only71% of crimes go reported. If ten crimesare randomly selected, find the probability that at most 2 are not reported. Round to the nearesthundredth of a percent.

• 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) Find the missing probability.

x p(x)

0 ?

1 0.23

2 0.08

3 0.04

4 0.44

Answer: 0.21

Process: The probabilities must add to 1.

2) Find the mean of the probability distribution.

x p(x)

0 0.1

1 0.1

2 0.1

3 0.2

4 0.15

5 0.3

6 0.05

Answer: 3.3

Process: Summate x times p(x).

3) 45% of college applicants into the UC system are accepted. If there are 200,000applicants, how many can be expected tobe accepted? What is the standard deviation.Round to the nearest hundredth.

Answer: 90,000 and 222.49

Process: Multiply n(p) to find the average.Multiply n(p)(q) and take the square root to find thestandard deviation.

4) If the variance of a probability distributionis 3.457, what is the standard deviation?Round to the nearest hundredth.

Answer: 1.86

Process: Square root the variance

SILVER

2 points

5) Find the standard deviation to the nearest hundredth.

x p(x)

0 0.11

1 0.21

2 0.4

3 0.12

4 0.10

5 0.04

6 0.02

Answer: 1.36

Process: There are 2 methods. The more common methodis to summate x2•p(x) and then subtract μ2. Then, squareroot.

6) The probability that a customer at a gasstation purchases diesel is 0.15. If six drivers pull into a gas station, find the probability that exactly 2 of them purchase diesel. Round to the nearesthundredth of a percent.

Answer: 17.62%

Process: Since the probabilities are independent…Use the binomial distribution formula.

6C2(0.15)2(0.85)4

7) The number of particles emitted froma radioactive source has an average of4 particle per minute. Find the probability that exactly 2 are emitted. Round to the nearesthundredth of a percent.

Answer: 14.65%

Process: Since there is an average over a given regionor period of time, use the Poisson formula.

8) A package of mixed nuts contains 20walnuts and 80 almonds. Five are grabbedin one handful. Find the probability that exactly one is a walnut. Round to the nearesthundredth of a percent.

Answer: 42.01%

Process: Since there is no replacement, use the hypergeometric formula. (20 choose 1)(80 choose 4)divided by (100 choose 5).

GOLD

3 points

9) Men’s Wearhouse got a shipment of90 suits. Eight of them are missing shoes.You randomly grabbed 6 suits. Find the probability that at least 5 have shoes. Round to the nearesthundredth of a percent.

Process: P(5 have shoes) + P(6) since you cannot choose more than 6 with shoes. Since there is no replacement, use the hypergeometric formula for P(5) and P(6).

Answer: 91.30%

10) According to police statistics, only71% of crimes go reported. If ten crimesare randomly selected, find the probability that at most 2 are not reported. Round to the nearesthundredth of a percent.

Answer: 40.99%

Process: Since the probabilities are independent…Use the binomial distribution formula for p(0) + p(1) + p(2)are not reported.

Answer: 11.06%

Tiebreaker) The probability of getting on the Wallof Fame is 0.04. You randomly select3 people from the class, find the probabilityexactly one person made the Wall of Fame.Say your answer as a percent roundedto the nearest hundredth of a percent.

HW

• P. 347 #1-11 (Skip 4, 9, 10)

• To study, look at this slideshow, past slideshows, the book, the chapter review, etc.

• Winners: Odds

• Test Tomorrow