Statistics and Probability Answers

For the following data compute variance and standard deviation.


2



9 1 81 9 81
8 2 64 16 128
7 3 49 21 147
6 3 36 18 108
5 5 25 25 125
4 3 16 12 48
3 2 9 6 18
2 1 4 2 4
1 2 1 2 2
0 1 0 0 0

24. For a given set of data m3 = 10.8 and m2 = 9.2; determine and explain the skewness of the distribution.
25. A given distribution has m4 = 108.8 and m2 = 8.0; determine and explain kurtosis of the distribution.

The average annual medical expense per family in a small city was Birr 750 in 1998. A random sample of 49 families was selected and their expenses for 1999 had a mean of Birr 800 with a standard deviation of Birr 140. Based on this information, can we conclude at α= 5% that the average annual medical expenses had increased from the 1998 average?

19. Let µ represent the population mean expenditure for 1999. Which of the following is the appropriate alternative hypothesis?
(A) µ ≠ 750 (B) µ = 750 (C) µ > 750 (D) µ < 750 (E) µ > 800

20. Which of the following is the appropriate rejection region?

(A) Z < –1.96 or Z > 1.96 (B) Z < –1.96 (C) Z < –1.645 (D) Z > 1.645
(E) –1.96 < Z < 1.96
21. Which of the following is the value of the test statistic?
(A) 50 (B) –0.36 (C) 0.36 (D) –2.5 (E) 2.5

A survey classified 200 students by gender and by their opinion on a certain issue. The number falling into the different categories are shown in the following table. A student is randomly chosen from the group.
Opinion
Gender For Against Total
Male 30 40 70
Female 50 80 130
Total 80 120 200

9. The probability that the student is female and is against the issue is

10. The probability that the student is male or is for the issue is

11. Given that the student chosen is for the issue, the conditional probability that the
student is male is

The probability that Martha will play soccer is 0.3, the probability that Ayyantu will play soccer is 0.4, and they make their decisions independently.

6. The probability that both of them will play soccer is

7. The probability that Martha or Ayyantu or both will play soccer is

8. The probability that both Martha and Ayyantu will not play soccer is

In bolt factory , machine A ,B ,and C manufacturer 25, 35 and 40

Percent of the total output , 5, 4 and 2 percent , respectively are

defective bolts.A bolts is selected at random and found to be defective.

What is the probability that the bolt came from machine A , B and C ?

A survey classified 200 students by gender and by their opinion on a certain issue. The number falling into the different categories are shown in the following table. A student is randomly chosen from the group.

Suppose the scores on an examination are normally distributed with a mean of 50 and a standard deviation of 10 for student population.

In order to estimate the mean diameter of a variety of orange, a sample of 25 oranges were selected and the sample mean was found to be 7.5 cm with a sample standard deviation of 1.5 cm.

A No Claims Discount system is operated by a car insurer. There are four levels of discount: 0%, 10%, 25% and 40%. After a claim-free year a policy holder moves up one level (or remains at the 40% level if they are already there). If a policy holder makes one claim in a year he or she moves down one level (or remains at the 0% level if already there). A policyholder who makes more than one claim in a year moves down two levels (or moves to or remains at the 0% level). Changes in level can only happen at the end of each year. The probability of a claim in any given month is assumed to be constant at 0.04 (i.e. 4%). At most one claim can be made per month and claims are assumed independent. Calculate the proportion of policyholders in the long run who are at the 25% level.

An article in Technometrics (1999, Vol. 41, pp. 202–211) studied the capability of a gauge by measuring the weight of paper. The data for repeated measurements of one sheet of paper are in the following table. Construct a 90% one-sided, upper confidence interval for the standard deviation of these measurements. Assume population is approximately normally distributed.

Round your answer to 3 decimal places.

3.481

3.448

3.485

3.475

3.472

3.477

3.472

3.464

3.472

3.470

3.470

3.470

3.477

3.473

3.474