A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with four different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts a-c.

a. There are __ different ways to appoint the officers.

b. How many different ways can the committee be​ appointed?

c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified​ candidates?

Use the given information to find the number of degrees of​ freedom, the critical values

chi Subscript Upper L Superscript 2χ2L

and

chi Subscript Upper R Superscript 2χ2R​,

and the confidence interval estimate of

sigmaσ.

It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.Nicotine in menthol cigarettes

9595​%

​confidence;

nequals=2727​,

sequals=0.240.24

mg.

LOADING...

Click the icon to view the table of​ Chi-Square critical values.

dfequals=nothing

​(Type a whole​ number.)

chi Subscript Upper L Superscript 2χ2Lequals=nothing

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

chi Subscript Upper R Superscript 2χ2Requals=nothing

​(Round to three decimal places as​ needed.)The confidence interval estimate of

sigmaσ

is

nothing

mgless than<sigmaσless than<nothing

mg.

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

1. A fair coin is tossed twice. Consider the following events:
a) A = a head on the first toss;
b) B = a tail on the first toss;
c) C = a tail on the second toss;
d) D = a head on the second toss.

Are events A and B mutually exclusive ? WHY or WHY NOT ?

Are events C and D Independent ? WHY or WHY NOT ?

2. Suppose there are 3 similar boxes. Box i contains i white ball(s) and two black balls. I pick one box at random, then pick a ball at random from the box. If the ball drawn is black, what is the probability that the ball came from Box i ?

( so, Box 1 contains 1 white ball and two black balls; Box 2 contains 2 white balls and two black
balls; Box 3 contains 3 white balls and two black balls.)

The heights of 2000 students are normally distributed with a mean of 165.5 centimeters and a standard deviation of 7.1 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights:

(a) less than 151.0 centimeters?

(b) Between 163.5 and 173.0 centimeters inclusive?

(c) Equal to 168.0 centimeters?

(d) Greater than or equal to 182.0 centimeters?

What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is used in a real-world scenario. Write a one to two (1–2) page short paper in which you answer the questions about distribution sampling

What is a Pre-test? Explain. What is a Post-test? Explain. Write a one to two (1–2) page paper in which you answer the questions about distribution sampling

It is said that more males register to vote in a national election than females. A research organization selected a random sample of 256 registered voters and reported that 136 of the registered voters were male.

a. Formulate the hypotheses for this problem.

b. Compute the standard error of .

c. Compute the test statistic.

d. Using the p-value approach, can you conclude that more males registered to vote than females? Let the significance level is 0.05

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.

(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)

P(0) =

P(1) =

P(2) =

P(3) =

P(4) =

(c) What is the expected number of parolees in Alice's group who will not be repeat offenders? (Round your answer to two decimal places.) parolees What is the standard deviation? (Round your answer to two decimal places.)

(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders?

Suppose the following data are product weights for the same items produced on two different production lines.

Test for a difference between the product weights for the two lines. Use α = 0.05.

State the null and alternative hypotheses.

H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0

H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0    

H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical.

H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.

H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.  

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

1) You measure 42 textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 9.6 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places.

__< μ < __

2) Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 70 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 17.2 and a standard deviation of 3.9. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
__ < μ < __

3) 44% of 84 delegates in a policitcal convention favored changing the rules to restrict the number of potential candidates. What is the 80% confidence interval for the population proportion.
Give your answers as decimals, to two places.

__ < p < __

What sport games does it have 8 or more than 8 teams in one group where a round robin game sequence takes place? (that is, the teams play against each other once or more than once) P.S. the game must still have more than three rounds after the round-robin part of the game.

18% of all Americans live in poverty. If 44 Americans are randomly selected, find the probability that

a. Exactly 8 of them live in poverty.  
b. At most 11 of them live in poverty.   
c. At least 6 of them live in poverty.   
d. Between 5 and 9 (including 5 and 9) of them live in poverty.

18% of all Americans live in poverty. If 44 Americans are randomly selected, find the probability that

a. Exactly 9 of them major in STEM.  
b. At most 12 of them major in STEM.  
c. At least 8 of them major in STEM.  
d. Between 9 and 13 (including 9 and 13) of them major in STEM.

4. Leslie has been tasked with putting together a statistical report regarding the use of a particular park in her hometown. Previous data shows that 72% of the residents living in the town visited the park in the last month. She wants to know the probability that more than 98 individuals in a random sample of 150 residents have visited the park in the last month. Please Answer A-C

(a) Based on the information given, is the sample proportion p̂ of residents who have visited the park in the last month approximately normally distributed? Check the appropriate conditions to justify your answer

(b) What is the sample proportion p̂ for Leslies sample of 150 residents? Round your answer to two decimal places?

(c) What is the probability that more than 98 individuals in the random sample of 150 residents have visited the park in the last month?

An environmentalist wants to find out the fraction of oil tankers that have spills each month.

Step 1 of 2 :  

Suppose a sample of 688688 tankers is drawn. Of these ships, 510510 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Enter your answer as a fraction or a decimal number rounded to three decimal places.