1. Suppose there is a 12.5% probability that a randomly selected person aged 35 years or older is a smoker. In​ addition, there is a 11.9% probability that a randomly selected person aged 35 years or older is female, given that he or she smokes.

What is the probability that a randomly selected person aged 35 years or older is female and smokes?

2. For the month of May in a certain​ city, 71​% of the days are cloudy. Also in the month of May

in the same​ city, 55​% of the days are cloudy and snowy.

What is the probability that a randomly selected day in May will be snowy if it is cloudy​?

3. For two​ events, A and​ B, ​P(A)equals=.2​, ​P(B)equals=.4​, and ​P(A∩​B)equals=. 1.

Find​ P(A|B).

Find​ P(B|A).

Are A and B independent​ events?

1. If a seed is planted, it has a 85% chance of growing into a healthy plant.

If 10 seeds are planted, what is the probability that exactly 2 don't grow?

2. A poll is given, showing 40% are in favor of a new building project.

If 6 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

3. A poll is given, showing 70% are in favor of a new building project.

If 10 people are chosen at random, what is the probability that fewer than 6 of them favor the new building project?

4. A poll is given, showing 30% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that greater than 6 of them favor the new building project?

A two-way table is given below, which shows the counts of the favorite leisure activities for 50 college students - 20 men and 30 women. Leisure Activity Yoga Sports TV Total Men 2 10 8 20 Women 16 6 8 30 Total 18 16 16 50 (a) What is the probability that a student selected at random is both a woman and student prefers Yoga? (b) What is the probability that a student is either a male or prefers sports? (c) What is the probability that a student selected at random prefers to watch television? (d) What is the probability that a female student selected at random, prefers television? (e) Draw the tree diagram for the above table. Be sure to label all probabilities.

Make an example of a binomial experiment and its binomial random variable X (Do not use a coin-flipping example, anything else is fine)

1. What is your trial? How many trials (which is n) do you have? Why do you think they are independent which is one of the required conditions for the binomial experiments?
2. Which outcome of your trial is considered a success?
3. The probability of having a success per trial, P. Give the probability value of P. If you are using an experimental (relative frequency) probability, use hypothetical numbers to derive the value of P.
4. You have n trials. How does P (X=1) differ from " the probability of having a success per trial, P" ? Explain.

The data in the table represents the breakdown of semiconductor wafers by lot and whether they conform to a thickness specification. If one wafer is selected at random, a) what is the probability that the wafer conforms to specifications? b) what is the probability that the wafer is from Lot A and conforms to specifications? c) what is the probability that the wafer is from Lot A or conforms to specifications? d) what is the probability that the wafer conforms to specifications, given the wafer is from Lot A? e) Are the events “from Lot A” and “conforms to specifications” independent? Why or why not? Use the results from some of the previous parts of this exercise to answer part e.

Make an example of a binomial experiment and its binomial random variable X (Do not use a coin-flipping example, anything else is fine)

1. What is your trial? How many trials (which is n) do you have? Why do you think they are independent which is one of the required conditions for the binomial experiments?
2. Which outcome of your trial is considered a success?
3. The probability of having a success per trial, P. Give the probability value of P. If you are using an experimental (relative frequency) probability, use hypothetical numbers to derive the value of P.
4. You have n trials. How does P (X=1) differ from " the probability of having a success per trial, P" ? Explain.

Suppose you have eight marbles in a bag - three that are green and five that are pink. Calculate the probabilities of each of the following events using the appropriate choice of either Equation (4.8) or Equation (4.10).

1. What is the probability that you draw a green marble, put it back, and then draw a pink marble?

2. What is the probability that you draw a green marble, do not put it back, and then draw a pink marble? [If you did not realize this already, somehow there has to be a difference between “replacement” versus “without replacement.”]

3. What is the probability that you draw two green marbles (without replacement)?

4. What is the probability that you draw two green marbles (without replacement) or you draw a green marble followed by a pink marble (without replacement)?

The average age of CEOs is 56 years. Assume the variable is normally distributed, with a standard deviation of 4 years. Give numeric answers with 4 decimal places.

a) If one CEO is randomly selected, find the probability that he/she is older than 63. Blank 1

b) If one CEO is randomly selected, find the probability that his/her mean age is less than 57. Blank 2

c) If one CEO is randomly selected, find the probability that his/her age will be between 53 and 59. Blank 3

d) If 36 CEOs are randomly selected, find the probability that their mean age is between 53 and 59. Blank 4

e) Explain the reason the answers to c) and d) above are differen

Diameters of mature Jeffrey Pine Trees are normally distributed with a mean diameter of 22 inches and a standard deviation of 6 inches. (Round your answers to four decimal places)

a. Find the probability that a randomly selected Jeffrey Pine tree has a diameter greater than 30 inches.

b. Find the probability that a randomly selected Jeffrey Pine tree has a diameter no more than 15 inches.

c. Find the tree diameter that defines the 60th percentile.

d. If 20 Jeffrey Pine trees are randomly selected find the probability that their mean diameter is at least 24 inches

e. If 55 Jeffrey Pine trees are randomly selected find the probability that their mean diameter is at between 22 and 24 inches.

A local grocery store owner wants to learn more about how many apples patrons buy from his store week to week, and he has asked for your help calculating some probabilities. He tells you that he believes the data to be normally distributed, and that the average amount of apples bought each week is 678.32 lbs. with a standard deviation of 53.98 lbs.

A) What is the probability that the store sells more than 750 lbs. of apples in a week?

B) What is the probability that the store sells less than 500 lbs. of apples in a week?

C) What is the probability that the store sells between 600 and 700 lbs. of apples?

D) What is the probability that the store sells exactly 678.32 lbs. of apples?