The average number of acres burned by fires in New Mexico County is assumed to be normally distributed with a mean of 9000 and a standard deviation of 695 acres. You are told that the probability of the number of acres burned between 9350-R and 9350+R is .7802. Find R. (Hint: Draw a picture to see the area along with the given probability. Can Goal-Seek or trial and error help you find the value of R?)

How would I solve for R using goal seek in excel

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of heart transplants performed per day in a country is about

eight

Find the probability that the number of heart transplants performed on any given day is​ (a) exactly

six

​(b) at least

seven

and​ (c) no more than

four

​(a)

​P(6​)=

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

A bag contains 9 red, 8 orange, and 6 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 17 jellybeans such that the number of red ones is 7, the number of orange ones is 7, and the number of green ones is 33? Express your answer as a fraction or a decimal number rounded to four decimal places.

A bag contains 9 red, 8 orange, and 6 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 17 jellybeans such that the number of red ones is 7, the number of orange ones is 7, and the number of green ones is 33? Express your answer as a fraction or a decimal number rounded to four decimal places.

Question 7

The following lists of data represent five separate departments' technicians overtime for a week. Which has the smallest standard deviation?

Select the correct answer below:

a)28, 26, 20, 17, 21, 29, 28, 28, 17, 22

b)14, 15, 15, 12, 11, 14, 11, 13, 14, 12

c)34, 26, 34, 26, 22, 34, 24, 26, 25, 24

d)21, 15, 14, 27, 21, 24, 27, 20, 20, 30

e)9, 17, 21, 9, 14, 18, 22, 10, 12, 16

Question 8

A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.

Drawing the Blue 2 is an example of which of the following events? Select all correct answers.

Select all that apply:

B AND O

R OR E

E′

B′

R AND E

O′

B AND E

Question 9

If A and B are events with P(A)=0.2, P(A OR B)=0.62, and P(A AND B)=0.18, find P(B).

Provide your answer below:

Question 10

The probability of buying a movie ticket with a popcorn coupon is 0.608. If you buy 10 movie tickets, what is the probability that 3 or more of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)

Provide your answer below:

P(X greater than or equal to 3)=

Question 11

At a certain company, the mentoring program and the community outreach program meet at the same time, so it is impossible for an employee to do both. If the probability that an employee participates in the mentoring program is 0.51, and the probability that an employee participates in the outreach program is 0.21, what is the probability that an employee does the mentoring program or the community outreach program?

Provide your answer below:

Question 12

A grain elevator measures the weight of each truck that delivers grain to their site. What is the level of measurement of the data?

a)Nominal

b)Ordinal

c)Interval

d)Ratio

Question 13

Let W be the event that a randomly chosen person works for the city government. Let V be the event that a randomly chosen person will vote in the election. Place the correct event in each response box below to show:

Given that the person works for the city government, the probability that a randomly chosen person has will vote in the election.

P(_ _ )

Question 14

Carlos and Devon both accepted new jobs at different companies. Carlos's starting salary is $42,000 and Devon's starting salary is $40,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers.

A website that collects salary information from a sample of employees for a number of major employers reports that Carlos's company offers a mean salary of $52,000 with a standard deviation of $8,000. Devon's company offers a mean salary of $48,000 with a standard deviation of $5,000.

Find the z-scores corresponding to each of their starting salaries. Round to two decimal places, if necessary.

Provide your answer below:

Carlos's z-score:

Devon's z-score:

Question 15

A deck of cards contains RED cards numbered 1,2,3,4,5, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN?

Select the correct answer below:

6/13

3/13

5/13

2/13

12/13

10/13

On a womens basketball team, one player can make 61% of free throws she attempts. A success is making a free throw (in basketball, "making a free throw" means the ball successfully went through the hoop.) The random variable X = the number of free throws made out of the seven attempted. Assume that outcomes of free throw attempts can be considered independent of each other. (a) What is the probability that in a given game, she attempts 7 free throws and makes 3 of them? (4 decimal places) (b) What is the probability that in a given game, she attempts 7 free throws and makes all of them? (4 decimal places) (c) What is the probability that in a given game, she attempts 7 free throws and makes 6 or fewer of them? (4 decimal places) (d) What is the mean (expected value) of number of free throws she makes in 7 attempts? (1 decimal place) (e) Of the choices listed below, which ones indicate that X is a binomial random variable? Select all that apply. X represents the number of failed free throws out of seven attempts. There are seven independent trials. There are two possible outcomes, success (making the free throw) and failure (not making the free throw) The probability of making a free throw is different in each trial. X represents the number of successful free throws out of seven attempts. The probability of making the free throw, 61%, is the same for each trial. If the player fails at the first attempt, she is less likely to successfully make the second and third attempts.

Problem #3

Faith and Healing.

A higher percentage of southerners believe in God and prayer, according to a

1998 study by the University of North Carolina’s Institute for Research in Social Science. The

survey was conducted by means of telephone interviews with 844 adults in 12 southern states and

413 adults in other states. One of the findings was that 46% of southerners believe they have been

healed by prayer, compared with 28% of others. Assume that the results of the UNC survey are the

true, population percentages for these regions. Suppose that 20 southerners are to be selected at

random and asked if they believe they have been healed by prayer. We are interested in the number

who answer “Yes” to this question.

a) What is an appropriate statistical model?

Clearly specify and define a random variable. (Let X = ...)

State the model, verify conditions, and identify all parameters.

b)Of the 20 southerners selected, what is the expected number of “Yes” responses? Write an

expected value statement, give the formula, give the formula with numbers plugged in, give

your final answer.

For parts c), d), e), and f) write a probability statement and give a numerical answer.

c) What is the probability that exactly 10 responded “Yes”?

d) What is the probability that between 10 and 15 (

both inclusive) responded “Yes”?

e) What is the probability that over 75% of the 20 responded “Yes”?

f) What is the probability that less than 8 responded “Yes”?

g) Suppose a sample of 100 non-southerners were to be selected at random and asked if they

believe they have been healed by prayer. What is the expected number of “Yes” responses

and what is the standard deviation for the number of “Yes” responses?

(1)Using the Matlab code developed in Software Assignment #1:

a. Convert the code that generates the random number (H,T) with equal probabilities into a function called myBernolli(p, S) that takes as an input the probability of success p and S is the outcome defined as success (either T or H) and returns the outcome of the trial (either T or H).

b. Test that your function is actually producing the successful outcome with probability p by running the function in a loop of 1000 trials and counting how many times success is produced (it should be close to p*1000).

c. Write a Matlab function called myBinomial(n,p) that takes as an input the total number of trials n, the probability of success p and the outcome defined as success S and uses myBernolli() to return as an output the number of successes x.

d. Write a Matlab function called myGeometric() that takes as an input the probability of success p and the outcome defined as success S and uses myBernolli() to return as an output the number of trials till first success x.

e. Verify that myBinomial() and myGeometric() generates values that follow Binomial and Geometric Distributions by running each of them 5000 times in a loop and plotting a histogram of the random variable x generated from each.

Hints: Random numbers with probability p are generated in Matlab using the command function rand(). Read the help on Matlab to know how to use the function by typing help rand in Matlab command line. Histogram plots [hist()] is a function in Matlab. Read its help to know how to produce

A component is purchased from 3 suppliers, A, B, and C, where the suppliers have

respective defective rates of 2%, 6%, and 4%. Of all the components purchased, 20%

comes from supplier A, 50% from supplier B, and 30% from supplier C, that is, each

shipment comes from each of these suppliers with these probabilities. The company uses

the following quality control policy. A sample of 15 units is randomly selected from each

shipment of components. If at most 2 defective units are found in the sample, then the

entire shipment is accepted; otherwise, the entire shipment is rejected.

Determine the following:

(a-1) probability that a shipment will be accepted given that it came from Supplier A.

(a-2) probability that a shipment will be accepted given that it came from Supplier B.

(a-3) probability that a shipment will be accepted given that it came from Supplier C.

(a-4) Using the law of total probability and your responses to parts (a-1)-(a-3) above,

determine the probability that a shipment will be accepted.

(b-1) expected number of defectives in a random sample of 15 units, if the shipment came

from Supplier A.

(b-2) expected number of defectives in a random sample of 15 units, if the shipment came

from Supplier B.

(b-3) expected number of defectives in a random sample of 15 units, if the shipment came

from Supplier C.

(b-4) Using the law of total expectation and your responses to parts (b-1)-(b-3) above,

determine the expected number of defectives in a random sample of 15 units.

Based on a​ poll, among adults who regret getting​ tattoos, 16 16​% say that they were too young when they got their tattoos. Assume that four four adults who regret getting tattoos are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.

a. Find the probability that none of the selected adults say that they were too young to get tattoos. ​(Round to four decimal places as​ needed.)

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. ​(Round to four decimal places as​ needed.)

c. Find the probability that the number of selected adults saying they were too young is 0 or 1. ​(Round to four decimal places as​ needed.)

d. If we randomly select four four ​adults, is 1 a significantly low number who say that they were too young to get​ tattoos? No, because the probability that at most 1 of the selected adults say that they were too young is greater than 0.05.