# Foundations of Probability and Statistics

Please see below. Can you write out the formula and how its done, I want to learn how these are done. Please take your time, in the past I have gone back over the work and I found that it was wrong. There is also an attachment so you can see it better, I would just go off the attachment instead, I just put it on here so people can easily view the problem. Thanks

15. In 2000, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2001, the average age was 24 with a standard deviation of 4.08. Using Coefficient of Variation determine in which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

2000 2001

Mean 22 24

Standard Deviation 3.96 4.08

Coefficient of Variation ? ?

Conclusion: _________________________________________________________________________

______________________________________________________________

__________________________________________________________________________

16. A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students.

40 25 35 30 20 40 30 20 40 10 30 20 10 5 20

Putting these hours in ascending order:

5 10 10 20 20 20 20 25 30 30 30 35 40 40 40

Using this data set, compute the

a. median =

b. mean =

c. mode =

d. 40th percentile

e. range =

f. Sumation X sqard =

( sumation X sqard) =

sample variance =

g.standard deviation =

21. In a large university, 15% of the students are female. If a random sample of twenty students is selected,

a. what is the probability that the sample contains exactly four female students?

Use the Formula

p = .15, q = .85, n = 20

P(4) =

b. what is the probability that the sample will contain no female students?

Use the Table

P(0) =

22. The random variable x has the following probability distribution:

x f(x)

0 .25

1 .20

2 .15

3 .30

4 .10

a.

b.Calculate the expected value of x.

Expected value = mean = u = Sumation XP(x) =

c.Calculate the variance of x.

Variance = o^2 = sumation(x-u)^2 P(x) =

25. A major department store has determined that its customers charge an average of $500 per month with a standard deviation of $80. Assume the amounts of charges are normally distributed.

a. What percentage of customers charges more than $380 per month?

P(x > 380) =

29. The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces.

a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces?

P(x greater than or equal to 4.14)

z =

P(x greater than or equal to 4.14) =

31. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

a. What is the probability that you will receive a Merit scholarship?

P(M or A) = P(M) + P(A) - P(M and A)

P(M) =

b. Are events A and M mutually exclusive? Why or why not? Explain.

c. Are the two events A and M independent? Explain using probabilities.

d. What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

P(A | M) =

32. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.

Selected Major

Gender Management Marketing Others Total

Male 40 10 30 80

Female 30 20 70 120

Total 70 30 100 200

a. What is the probability of selecting an individual who is majoring in Marketing?

P (Mktg) =

b. What is the probability of selecting an individual who is majoring in Management, given that the person is female?

Let Mgt = Majoring in Management, and F = Female

P(Mgt F) =

33. A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

This means find when {N} N=10, n = 3

n

#### Solution Preview

note for #16:

Median = point where half the data points are above it (for example, in 2,3,6 ; median = ...