MAT 107 Test #2                                          NAME:

Directions: Read and answer each question carefully. Do NOT remove the staple! Use backs of pages if necessary. Show all work! Probabilities should be carried out to 3 decimal places or left as fractions. Circle or box your answers!

 

  1. A recent study at a New England university found that 60% of all students missed class during the semester because of drinking. A random sample of 20 students is taken. Find the probability more than 15 students missed class because of drinking? Find the probability less than 5 students missed class because of drinking? Find the probability between 5 and 15 (inclusive) students missed class because of drinking. What are the mean and standard deviation of the number of students who missed class because of drinking from the sample.

 

  1. Consider the following data from the study on binge drinking, about number of hangovers per semester. Find the probability that a randomly selected student:

a.         Is male.

b.         Is both female and had no hangovers

c.         Had a hangover twice or more, given she is female.

d.         Is male, given he had only one hangover.

e.         Are being Male and having one hangover independent?

           

Number

Of

Hangovers

Gender

None

One

Two or More

Male

61

23

40

Female

66

25

36

 

  1. The weight of 18 year old males in Anchorage, Alaska is normally distributed with mean 175 lbs and a standard deviation 30 lbs. A randomly selected 18 year old male from Anchorage is selected. What is the probability he weighs less than 137 lbs? What is the probability he weighs more than 215 lbs? What is the probability he weighs between 137 lbs and 200 lbs? Find the weight, w, such that only 10% of the males from Anchorage weigh more than w.

 

  1. A casino devises a new game such that your winnings based on a $5 bet are given by the probability distribution below, where x is your winnings. You bet $5. What is probability you win $5? What is the probability you do not win $10? What is the probability you do not lose money? What are your expected (mean) winnings?

     

X

-5

0

5

10

p(x)

0.40

0.25

?

0.10

 

Answers:

1.   P( X > 15) = 0.050, P( X < 5) = 0.000, P(5 <= X <=15) = 0.949

      μ = 20 * .6 = 12, σ = sqrt( 20* .6 * .4) = 2.191

 

2.   P(male) = 124/251, P(female ∩ None) = 66/251

      P(Twice | Female) = 36/127, P(Male | One) = 23/48

      Male and One are not independent, P(male) * P(one) not = P(male ∩one)

      P(one) = 48/251, P(male) * P(one) = .094, P(male ∩one) = .092

 

3.   P( X < 137) = P( Z < -1.27) = .1020

      P( X > 215) = P( Z > 1.33) = .0918

      P(137 < X < 200) = P(Z < 0.83) – P(Z < -1.27) = .7967 - .1020 = .6947

      P( Z > 1.28) = .10, w = 1.28*30 + 175 = 213.4

 

4.   P(X = 5) = .25

      P((X = 10)’ ) = 1 - .10 = .90

      P(X >= 0) = 1 - .40 = .60

      E(X) = -5*.40 + 0*.25 + 5*.25 + 10*.10 = .25