Posted: February 10th, 2022

Stats Hw

I. Choose the best answer for each multiple choice. Please use CAPITAL letters to indicate your answer and write neatly. (20 points)

1. _C___ 3.__D__ 5. _A___ 7.__A__ 9. __D__
2. _C___ 4.__C__ 6. _D___ 8.__D__ 10. __A__

1. A numerical value used as a summary measure for a sample, such as sample mean, is known as a
A. population parameter
B. sample parameter
C. sample statistic
D. population mean

2. Which of the following statements about a discrete random variable and its probability distribution are true?
A. Values of the random variable can never be negative.
B. Some negative values of f(x) are allowed as long as ∑f(x) = 1.
C. Values of f(x) must be greater than or equal to zero.
D. The values of f(x) increase to a maximum point and then decrease.

3. The numerical value of the variance
A. is always larger than the numerical value of the standard deviation
B. is always smaller than the numerical value of the standard deviation
C. is negative if the mean is negative
D. can be larger or smaller than the numerical value of the standard deviation

4. The median of a sample will always equal the
A. mode
B. mean
C. 50th percentile
D. All of the above answers are correct

5. In a standard normal distribution, the probability that Z is greater than 0.5 is
A. 0.5
B. less than 0.5
C. at least 0.5
D. 1.96

6. The expected value of the random variable is
A. the standard error
B. the sample size
C. the size of the population
D. None of these alternatives is correct.

7. Suppose in a large firm, the pool of applicants for the positions of sales manager and sales associate consists of three men and three women. If each candidate has an equal chance of being selected, what is the probability that both positions will be filled by men?
A. 0.20
B. 0.25
C. 0.33
D. 0.50
8. The standard deviation of a sample was reported to be 20. The report indicated that = 7200. What has been the sample size?
A. 16
B. 17
C. 18
D. 19

9. From a group of 10 students, we want to select a random sample of 4 students to serve on a university committee. How many different random samples of 4 students can be selected?
A. 720
B. 5040
C. 210
D. 295

10. A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within 2 of the population mean?
A 0.683
B. 0.341
C. 0.954
D. Since the mean is not given, there is no answer to this question.

II. Problem Solving

1. The average lifetime of a light bulb is 3,000 hours with a standard deviation of 700 hours. A simple random sample of 49 bulbs is taken.

a. What is the expected value, standard deviation, and the shape of the sampling distribution of the average life of the light bulb? (5 points)
– 116 and bell shape like normal distribution

b. What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours? (10 points)
– 0.0482=4.82%
2. A private research organization studying families in various countries reported the following data for the amount of time 4-year-old children spent alone with their fathers each day.

Country Time with Dad
(minutes)
Belgium 30
Canada 44
China 54
Finland 50
Germany 36
Nigeria 42
Sweden 46
United States 42

a. Find the mean. (7 points)
– 43
b. Find the median. (7 points)
– 43
c. Find the mode. (5 points)
– 42
d. Find IQR. (10 points)
– 11.5
3. The average number of calls received by a switchboard in a 30-minute period is 10.

a. What is the appropriate probability distribution for X? (8 points)
– P(X=x)= e-1010x/x!
b. What is the probability that between 10:00 and 10:15 the switchboard will receive fewer than 3 calls? (12 points)
– 0.012465=1.24%
4. A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10.

a. The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? (8 points)
– 87.5
b. If 12.1 percent of her students failed the course and received F’s, what was the maximum score among those who received an F? (8 points)
– 66.3

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I. Select the best answer from each multiple-choice question. Please write neatly and in CAPITAL letters to convey your response. (20 pts.)

1. C___ 3. D__ 5. A___ 7. A__ 9. D__

2. _C___ 4. _C__ 6. _D___ 8. _D__ 10.

1. A numerical number used as a summary measure for a sample, such as sample mean, is referred to as a summary measure.

A. population factor

B. the sample parameter

C. the sample statistic

D. population average

2. Which of the following statements concerning a discrete random variable and its probability distribution is correct?

A. The random variable’s values can never be negative.

B. Some negative f(x) values are permitted as long as f(x) = 1.

C. f(x) values must be larger than or equal to zero.

D. The figures

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