 # Ten Statistics Questions and their solutions

10 Statistics Questions - See attached file for questions in proper formatting

1)Draw a standard normal density curve to represent each of the following. Use the standard normal distribution table to find the:
a. Area under the curve between z=0 and z = 2.33
b. Area under the curve between z=0 and z = -1.06
c. Area under the curve to the right of z = .28
d. Area under the curve to the left of z = -.53
e. Area under the curve between z=1.26 and z = 2.10

2)Create a sample space of possible outcomes for the following: flipping one coin and rolling an octagonal die. Find the probability of getting a compound event of heads and rolling a 7.
A random study of recent graduates' average grades and degrees showed the following results.
Degree
C
B
A
B.S.
6
9
13
B.A.
5
12
10

3)If a graduate is selected at random, find these probabilities. The graduate has a B.S. degree, given that he or she has an A average.
a. Given that the graduate has a B.A. degree, the graduate has a C average.
b. What is the probability that a person has a B.S. degree and a B?
c. What is the probability that a graduate has neither an A nor a C.

4)Working Mom’s Journal" reported that the mean time a mother, with her small children, spends in at the convenience store is 7.3 minutes. A sample of 20 moms is chosen from your neighborhood, and it is found that the mean time they spend in a convenience store was 8.2 minutes with a standard deviation of 1.4 minutes. Using , test the claim that the average amount of time a mom and her children spend in a convenience store is greater than 7.3 minutes.
a. Determine which test statistic you will use: the standard normal distribution, or the student’s t distribution. Explain why you chose this test statistic.
b. Establish the null and alternative hypotheses, state the claim.
c. Test the claim at and discuss your results, should you reject or not reject the null hypothesis, should you reject or except the claim.

5)From a sample of ten full-time staff, chosen from the education department at your school, it is found that their mean salary is \$50,340. Assume the standard deviation of the population is given as \$15,320. Find the 95% confidence interval for the population mean, give the margin of error and discuss your results.

6)Create a sample space for tossing a coin four times. Find the probability of getting a simple event of three heads and one tail.

7)Three cards are drawn, without replacement, from a standard deck of fifty-two cards. Find the probability of these events.
a. Getting three kings.
b. Getting a ten, nine, and eight in order.
c. Getting a diamond, heart, and club in order.
d. Getting three diamonds.
e.

8)In a doctor’s office there are eight nurses and four physicians. Seven nurses and two physicians are females. If a person is selected from the doctor’s office, find the probability that the person is a nurse or a male.
Staff
Females
Males
Total
Nurses
7
1
8
Physicians
2
2
4
Total
9
3
12

9)Discuss type I and type II errors in hypothesis testing. Give an example of each type of error.

10)A retail men’s clothing store owner buys from three companies: X, Y and Z. The recent most purchases are shown here.
Product
Company X
Company Y
Company Z
Shirts
33
26
41
Ties
53
23
38
If one item is selected at random, find these probabilities.
a. It was purchased from company X or is a shirt.
b. It was purchased from company Y or company Z.
c. It is a tie or was purchased from company X.

Full details along with solutions are presented.

Question Files
Ward_statistics.pdf

Subjects: Statistics
Topic: College Level Stats, Probability Functions, Type I/II Errros
Level: College / University
Tags:

### Stats Questions

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Project Details
Question Files
Ward_statistics.pdf

Subjects: Statistics
Topic: College Level Stats, Probability Functions, Type I/II Errros
Level: College / University
Tags:

## Stats Questions

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