Alex challenged David to a free-throw duel. Alex and David would take turns shooting free throws until someone makes a shot. David makes free throws with probability 0.9. Alex makes free throws with probability 0.45. Assume independence. Round all your answers to 4 decimal places.

a. If David shoots first, what is the probability that Alex is the first one to make a free throw?

b. Alex likes to complain. He says that he should shoot first since his success rate is lower. If Alex shoots first, what is the probability that Alex is the first one to make a free throw?

c. Alex does like to complain. He says that he should have two attempts for each one of David's attempts since his success rate is half of David's. What is the probability that Alex is the first one to make a free throw with these rules? That is, the pattern of attempts is AADAADAAD… instead of ADADAD… in part (b).

-Report the probability distribution as a table.

-The probability that X is less than Value 1 (or P(X < X Value 1)
-The probability that X is less than or equal to Value 2 (or P(X ≤ X Value 2)

-The probability that X is greater than Value 3 (or P(X > X Value 3)
-The probability that X is greater than or equal to Value 4 (or P(X ≥ X Value 4)

(Choose any four values for Value 1, Value 2, Value 3, Value 4)

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 159 lb and a standard deviation of 26.6 lb.

A. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 201 lb.The probability is approximately______?

​(Round to four decimal places as​ needed.)

B. If 40 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 201 lb.The probability is approximately______?

​(Round to four decimal places as​ needed.)

C. When redesigning the ejection​ seat, which probability is more​ relevant?

A.Part​ (a) because the seat performance for a single pilot is more important.

B.Part​ (b) because the seat performance for a single pilot is more important.

C.Part​ (a) because the seat performance for a sample of pilots is more important.

D.Part​ (b) because the seat performance for a sample of pilots is more important.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.8 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately________. ​

(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 130 lb and 171 lb.

The probability is approximately________.

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A. Part​ (b) because the seat performance for a sample of pilots is more important.

B. Part​ (b) because the seat performance for a single pilot is more important.

C. Part​ (a) because the seat performance for a single pilot is more important.

D. Part​ (a) because the seat performance for a sample of pilots is more important.

Question 1: Assume that the random variable X is normally​ distributed, with mean that = 47 and standard deviation that = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

P(X< AND = TO 43)

Using technology, what is P(X< AND = TO 43) equal? (round to four decimal places)

• How did you find this answer using a graphing calculator??

Question 2: The mean incubation time for a type of fertilized egg kept at 100.8​°F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days.

(a) What is the probability that a randomly selected fertilized egg hatches in less than 20 ​days?

​(b) What is the probability that a randomly selected fertilized egg takes over 24 days to​ hatch?

​(c) What is the probability that a randomly selected fertilized egg hatches between 18 and 22 ​days?

​(d) Would it be unusual for an egg to hatch in less than 17 ​days? Why?

• How did you find these answers? Thanks!

1. A country club has a membership of 500 members and operates facilities that include a swimming pool and a gymnasium. The club president would like to know how many members regularly use the facilities. A survey of the members indicates that 70% regularly use the swimming pool (S), 50% regularly use the gymnasium (G), and 5% use neither of these facilities regularly. Calculate the probability of the club members who use the facilities of the swimming pool and gymnasium P(S∩G).           

2. In Mr. ERIZ’s class, the probability of student who likes Mathematics subject is 0.5 and the probability who likes both Mathematics and Statistics subjects is 0.25.

1. If one student is chosen at random, what is the probability that this student likes Statistics given that he/she also like Mathematics subject?

2. If the probability of students who likes Statistics is 0.45, are the events ‘like Mathematics subject’ and ‘like Statistics subject’ independent? Justify your answer.                                                                                        

(4 marks)

3. Are the events ‘likes Mathematics’ and ‘likes Statistics’ mutually exclusive? Justify your answer.

An attorney in the Washington Metropolitan area has been in the law profession for several years. Over the years it is known that she has won 60% of all her cases representing her clients. She currently has 15 cases pending. Answer the following questions. Show what you put into the calculator and possible calculations for each part, not just the answers. Think binomial. Use the TI 83 showing all your work.

a. Probability that she will win 10 cases?

b. What is the probability that she will win less than 4 cases?

c. What is the probability that she will win at least 9 cases?

d. What is the probability that she will win more than 8 cases?

e. What is the probability that she will win at most 12 cases?

There are 23 students in a Statistics class. If the mean age of 22 of these students in the class is 22.5 years, find the age of the 23^rd student if the mean age of all the 23 students in the class is 23 years?

PKU is a rare, fully penetrant, autosomal recessive condition in which an affected individual cannot break down the amino acid phenylalanine. Neither Brian nor Mary has PKU, and they want to have children. They are concerned because Brian's father has PKU, and while neither of Mary's parents has PKU, her brother has PKU. Use symbols A and a.

1) What is the probability that Mary and Brian's first child will have PKU? Show work.
2) Mary and Brian have a child, and it does not have PKU. They decide to have a second child. Does knowing the phenotype of the first child cause you to change the probability you calculated in question 1 to predict the probability the next child will have PKU? If not, why?
3) Consider an alternate scenario where Mary and Brian have a child and it does have PKU. They decide to have another child. Does knowing the phenotype of the first child change the probability you calculated in 1 to predict the probability the next child will have PKU? If not, why?

An observational study of a group of students was conducted, and students were classified in two ways. First, they were each classified as to whether or not they were FullTime or PartTime. Second, they were each classified as to which of two colleges they were in, COS (college of sciences) or CBA (college of business administration). From that data, the following partial joint probability table was constructed.

Please answer the following questions about the probability of drawing students at random from this group according to the table above.  Please keep your answers as fractions (e.g., "3/7").

• What is the marginal probability that a random student will be from COS (college of science)?  
• What is the joint probability that a random student will be both part-time and from CBA (college of business administration)?
• If I already know the student is from CBA, what is the probability they are a full time?