Homework Answers

A poll is given, showing 35% are in favor of a new building project.

If 9 people are chosen at random, what is the probability that at least 5 of them favor the new building project? 

Probability =    (Please show your answer to 4 decimal places)

Suppose that about 77% of graduating students attend their graduation. A group of 33 students is randomly chosen, and let X be the number of students who attended their graduation.

1. What is the distribution of X? X ~ 
2. ? B U N 
3.  (,) 
4. Please show the following answers to 4 decimal places.
5. What is the probability that exactly 25 number of students who attended their graduation in this study? 
6. What is the probability that less than 25 number of students who attended their graduation in this study? 
7. What is the probability that at most 25 number of students who attended their graduation in this study? 
8. What is the probability that between 20 and 26 (including 20 and 26) number of students who attended their graduation in this study? 

A poll is given, showing 80% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that fewer than 5 of them favor the new building project? 

Probability =    (Please show your answer to 4 decimal places)

Assume Binomial Distribution with n = 10 and p = 0.6. Please show your answers to 4 decimal places.

P(X = 4) =  

P(X ≤ 4) =   

P(X < 4) = 

P(X >4) =   

P(X ≥ 4) = 

According to the American Red Cross, 8.9% of all Connecticut residents have Type B blood. A random sample of 16 Connecticut residents is taken.

X = the number of CT residents that have Type B blood, of the 16 sampled.

What is the expected value of the random variable X?

A binomial experiment consists of 11 trials. The probability of success on trial 4 is 0.46. What is the probability of success on trial 8?

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

Too SmallToo LargeTotalLow Income172340High Income251035Total423375

Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimal places. Give your to part d as a whole number.)

a) The proportion of all children that drew the nickel too small is:     

Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children.

b) If 5 children are chosen, the probability that exactly 2 would draw the nickel too small is:    

c) If 5 children are chosen at random, the probability that at least one would draw the nickel too small is:    

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

Too SmallToo LargeTotalLow Income172340High Income251035Total423375

Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimal places. Give your to part d as a whole number.)

a) The proportion of all children that drew the nickel too small is:     

Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children.

b) If 5 children are chosen, the probability that exactly 2 would draw the nickel too small is:    

c) If 5 children are chosen at random, the probability that at least one would draw the nickel too small is:    

A company prices its tornado insurance using the following assumptions:

• In any calendar year, there can be at most one tornado. 

• In any calendar year, the probability of a tornado is 0.04. 

• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.

Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 16-year period.