Consider the approximately normal population of heights of female college students with a mean μ = 69.5 inches and a standard deviation σ = 3 inches. A random sample of 36 females is obtained.

a. What is the probability that an individual height of a female college student, x, is at least 70 inches? Mark and label the mean μ along with the x value then shade the area defining the probability of interest on the graph A. Mark and label the z-score then shade the area defining the probability of interest on the graph B.

b. What is the probability that the sample mean height of female college students, ?̅, is at least 70 inches? Mark and label the mean ?x̅ along with the ?̅ value then shade the area defining the probability of interest on the graph A. Mark and label the z-score then shade the area defining the probability of interest on the graph B.

Conditional Probability

total A survey asked 300 Adults and Children which of three cereals they would like to have for breakfast. Use the results in the table to answer the given problems. [You do not have to simplify.]

[1] Find the probability that a person prefers Frosted Flakes

[2] Find the probability that a Child does NOT want Bran Flakes.

[3] Find the probability that someone prefers Frosted Flakes given that the person is an Adult.

[4] Find the probability that a person does NOT prefer Bran Flakes.

[5] Find the probability that an Adult prefers Frosted Flakes or Cocoa Puffs.

When someone buys a ticket for an airline​ flight, there is a 0.0986 probability that the person will not show up for the flight. A certain jet can seat 12 passengers. Is it wise to book 14 passengers for a flight on the​ jet? Explain Determine whether or not booking 14 passengers for 12 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet.

A. It is not a wise decision because the probability that there are not enough seats on the jet is...........​So, overbooking is not an unlikely event.

B. It is a wise decision because the probability that there are not enough seats on the jet is............. ​So, overbooking is an unlikely event.

C. It is a wise decision because the probability that there are not enough seats on the jet is............ ​So, overbooking is not an unlikely event.

D. It is not a wise decision because the probability that there are not enough seats on the jet is.......... ​So, overbooking is an unlikely even

According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 230 executives are randomly surveyed. Appendix A Statistical Tables a. What is the probability that fewer than 101 of the executives believe employees are most productive on Tuesdays? b. What is the probability that more than 115 of the executives believe employees are most productive on Tuesdays? c. What is the probability that more than 96 of the executives believe employees are most productive on Tuesdays?

a. What is the probability that fewer than 101 of the executives believe employees are most productive on Tuesdays?
b. What is the probability that more than 115 of the executives believe employees are most productive on Tuesdays?
c. What is the probability that more than 96 of the executives believe employees are most productive on Tuesdays?

Show how to compute the probability of winning the jackpot in the megamillions lottery. The rules are at http://www.megamillions.com/how-to-play under ”How to play”. (a) First let us define an appropriate sample space Ω where Ω = {(i1, i2, i3, i4, i5;i6)|what has to hold about i1, . . . , i6}? (b) How many outcomes are in Ω? (c) What is the probability of winning the jackpot? (d) Do you have a better chance of winning the jackpot in powerball or in megamillions? (e) Consider the probability of flipping a fair coin n times and getting heads every time. (So if n = 3, the probability is 1/8th.) How large does n need to be before the probability becomes smaller than the probability of winning the jackpot in megamillions?

Sparagowski & Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average time between placing an order and receiving the order at McDonald's restaurants was 2.78 minutes (The Cincinnati Enquirer, July 9, 2000). Waiting times, such as these, frequently follow an exponential distribution.

1. What is the probability that a customer's service time is less than 2 minutes?

2. What is the probability that a customer's service time is more than 5 minutes?

3. What is the probability that a customer's service time is more than 2.78 minutes?

4.What is the probability that a customer's service time is less than 30 seconds?

5. What is the probability that a customer's service time is exactly 45 seconds?

6. What is the probability that a customer's service time is more than 42 seconds?

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.5 non-work-related e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.

A. What is the probability Linda Lahey, company president, received exactly 4 non-work-related e-mails between 4 P.M. and 5 P.M. yesterday? (Round your probability to 4 decimal places.)

B. What is the probability she received 6 or more non-work-related e-mails during the same period? (Round your probability to 4 decimal places.)

C. What is the probability she received four or less non-work-related e-mails during the period? (Round your probability to 4 decimal places.)

R studio: Show detailed working, including appropriate mathematical notation for each question. For most questions this will involve showing your working from R, (e.g. cut-and-paste commands and output from an R session).

The probability of a student owning a cat is known to be 0.44; and the probability of a student owning a dog is known to be 0.54. If the probability of owning both is known to be 0.36, calculate:

(a) the probability of not owning a dog

(b) the probability of owning either a cat or a dog or both

(c) the probability of a student owning a dog, given that they own a cat

(d) Are owning a cat and dog independent? Justify (e) (harder) a group of 32 vetinary science students is interviewed. Of these 32, only 7 have no pet. State a sensible null hypothesis, test it, and interpret.

There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.5, P(F) = 0.3, and P(E ∩ F) = 0.12.

(a) What is the probability that the individual must stop at at least one light; that is, what is the probability of the event P(E ∪ F)?


(b) What is the probability that the individual doesn't have to stop at either light?


(c) What is the probability that the individual must stop at exactly one of the two lights?


(d) What is the probability that the individual must stop just at the first light? (Hint: How is the probability of this event related to P(E) and P(E ∩ F)? A Venn diagram might help.)

Show all of your work. No credit will be given if there is no work. Simplify if possible, unless noted.

Setup:

• Suppose the probability of a part being manufactured by Machine A is 0.4

• Suppose the probability that a part was manufactured by Machine A and the part is defective is 0.12

• Suppose the probability that a part was NOT manufactured by Machine A and the part IS defective is 0.14

Questions To Answer: 1. (2 pts) Find the probability that a part is defective given that it was made by Machine A.

2. (2 pts) Find the probability that a part is defective.

3. (4 pts) Are the states of a part being made by Machine A and being defective independent? Circle your answer and state your reason. YES, they are independent NO, they are NOT independent Reason:

4. (2 pts) Find the probability that Machine A produced a specific part, given that the part was defective. Round your final answer to 2 decimals, if needed.