Statistics and Probability Answers

The following were the scores obtained by Form II students in a Mathematics 

49

63

59

58

44

49

51

62

37

30

49

45

52

50

42

54

32

57

41

42

56

44

46

63

44

40

50

46

53

48

37

46

53

68

66

58

36

40

56

37

66

43

40

43

51

59

42

52

46

57

Required

a)     Group the data into 7 classes and Make a grouped frequency distribution          

 b)      70^th percentile mark                                                                                       

 c)   Standard deviation                                                                                        

Comment on the distribution of marks       

The geometric distribution with parameter p represents the number of failures in asequence of independent Bernoulli trials before a success occurs. Show that this distribution is of the exponential family

Ten competitors in a music competition are ranked by three adjudicators in the following order.

Competitor

  Competitor

A

B

C

D

E

F

G

H

I

J

Adjudicator 1

Adjudicator 2

Adjudicator 3

1

3

6

6

5

4

5

8

9

10

4

7

3

7

1

2

10

2

4

2

3

9

1

10

7

6

5

8

9

8

 Use Spearman’s rank order correlation technique  to compute:

i)       The pair of adjudicators who have the nearest approach to common tastes in music festival and therefore give the higher correlation between them.                         (3 marks)

ii)     The pair of adjudicators who have the worst taste of music and post the worst correlation.                                                                                                                                 (3 marks)

iii)   The average correlation amongst the three adjudicators.                              (2 marks)

a studied ,the average number of the heirs bond for the senior high school students for their online classes a week is 24 hours with a standard deviation of 4 hours .as shown in the study is true and a data is normally distributed

A. find the probability that a randomly selected senior high school students spend more than 26 our but less than 20 hours and

B

find the probability that a randomly selected senior high school students spend less than 21 hours or greater than 30 hours

C. Find the probability that a random sample of 12 senior highschool students spends more than 24 hours.

A large retailer wants to estimate the proportion of Hispanic customers in a particular state. First, think about how large a sample size (of the retailer’s customers) would be needed to estimate this proportion to within 0.04 accuracy and with 99% confidence. Assume there is no planning value for p* available. IF you decided to go for 0.01 accuracy instead of 0.04 accuracy?

A random sample is drawn from a population of known standard deviation 11.3. Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used).

n = 36, x ̅=105.2, s = 11.2

n = 100, x ̅=105.2, s = 11.2

In a Math Test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at a random will lie above score 50?

The mean height of grade 9 students at a certain high school is 164 centimeters and the standard deviation is 10 centimeters. Assuming the heights are normally distributed, What percent of the heights is greater than 168 centimeters? 

The probabilities of a machine manufacturing 0,1,2,3,4 or 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01, and 0.005, respectively. Find the mean, variance and standard deviation of the probability distribution. Round your answer to the nearest hundredths. 

The probabilities of a machine manufacturing 0,1,2,3,4 or 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01, and 0.005, respectively. Find the variance.