Project #32352 - Data management

In order to earn full marks on the questions, you must show all your work.

Part A: Communication

[5]

0.

A maximum of 5 marks will be earned, based on the presentation of your solutions. Keep in mind all the techniques for excellent mathematical work that have been discussed and demonstrated.

     

Part B: Knowledge

Provide only the answer for each of the following questions.

[2]

1.

The faces of an 8-sided die are numbered from 1 to 8. What is the probability of rolling a 4 six times in ten rolls?

[1]

2.

A certain type of light bulb has a failure rate of 5.6%. What is the expected number of failures if 700 light bulbs are tested?

 

[2]

[2]

3.

A 14-member committee for a fundraiser will be selected from a pool of 20 men and 15 women.

a)      What is the probability the committee will be equally split with men and women?

b)      What would be the expected number of men on the committee?

[2]

4.

A sample of 25 data pieces has a mean of 65.2. Find the value of x that has a standard deviation of 3.6.

 

[2]

[2]

5.

Find the corresponding z-score for each of the following raw scores, given the mean and the standard deviation.

a)      x = 9, µ = 10.5, σ = 2.1

b)      x = 500, µ = 300, σ = 250

     

Part C: Application

     
     

 

6.

A co-ed soccer team has 9 women and 7 men on its roster.  6 players play on the field at one time.

[2]

a)

What is the probability the starting lineup will have 3 men and 3 women on it?

[3]

b)

What is the probability the starting lineup will have at least 5 men on it?

[2]

c)

What is the expected number of women on the team?

 

7.

speed trap on the highway set by the O.P.P. shows that the mean speed of cars is 103.4 km/h with a standard deviation of 9.8 km/h.  The posted speed limit on the highway is 100 km/h.

[2]

a)

What percentage of drivers are technically driving under the speed limit?

[2]

b)

Speeders caught traveling 25 km/h or more over the speed limit are subject to a $5000 fine.  What percentage of speeders will be fined $5000?

[2]

c)

Police officers tend not to pull over drivers between 100 km/h and 110 km/h.  What percentage of drivers is this?

[2]

d)

The top 2% of all drivers speeding are subject to losing their license. According to the data, what speed must a driver be traveling to lose his or her license?

 

8.

A lacrosse team has been in its premier league for the last 47 seasons. During this time they have a mean number of wins of 17.3 and a standard deviation of 2.2 wins.

[2]

a)

What is the probability of the lacrosse team getting 21 wins in the upcoming season?

[2]

b)

What is the probability of the lacrosse team getting between 15 and 18 wins?

 

9.

A cruise ship has a 74% chance of having leftover rooms the week before the cruise. There are 25 cruise ships setting sail this month.

[2]

a)

Is it possible to approximate this binomial distribution using a normal approximation?

[2]

b)

What is the mean and the standard deviation for this approximation?

[2]

c)

What is the probability that exactly 20 cruise ships will have leftover rooms using the normal approximation?

[2]

d)

How different is the normal approximation from the binomial distribution value? Calculate the probability that exactly 20 cruise ships will have leftover rooms using the binomial method.

Part D: Thinking/Inquiry

 

 

10.

A game of chance requires the player to throw a 6-sided die and a 12-sided die.

[5]

a)

Create a probability histogram for this distribution.

[3]

b)

The player pays $5 to play and wins $10 for any odd roll and wins nothing for any even roll.  Calculate the expected winnings for the player and determine if this is a fair game or not.

 

11.

When two teams battle in a championship final, the Stars have a 54% chance of winning a game when playing at home and the Pros have a 57% chance of winning a game when playing at home. In a best-of-three matchup, the first game will be played at the Stars home field, the second game at the Pros home field and the third game back at the Stars home field.

[1]

a)

What is the probability the Stars win the final in two straight games?

[1]

b)

What is the probability the Pros win the final in two straight games?

[1]

c)

What is the probability the Stars win the final in three games?

[1]

d)

What is the probability the Pros win the final in three games?

     

Subject Mathematics
Due By (Pacific Time) 06/03/2014 01:59 pm
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