Statistics and Probability Answers

What is time series? What are the components of time series.

Calculate the correlation coefficient of the following data: x 45 46 46 47 48 49 50 y 44 48 45 48 52 51 49

X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book. A problem is selected at random. What is the probability that at least one of them will solve the same?

The manufacturer of television tubes knows from the past experience that the average life of tube is 2000 hrs with a s.d. of 200 hrs. A sample of 100 tubes has an average life of 1950 hrs. Test at the 0.01 level of significance to see if this sample came from a normal population of mean 2000 hrs.

An experiment was conducted to investigate the effect of two treatment T1, T2 on wheat growth. The experiment was carried out in two fields. 40 randomly selected plants were treated(20 with T1 and 20 withT2) in each field. The height of the mature plants were recorded as below (in cms). The interset is to answer the following questions.

1) Do the treatments appear to differ in their effect on the growth?

2) Is growth different in the fields?

3) Does the difference between the treatment differ between two fields?

Field 1 (Treatment 1)

90, 123, 108, 93, 100

108, 47, 105, 94, 123

90, 87, 124, 90, 77

110, 65, 93, 54, 60

Field 2 (Treatment 1)

56, 70, 66, 78, 74

72, 108, 87, 99, 61

98, 50, 53, 78, 76

74, 87, 81, 67, 61

Field 1 ( Treatment 2)

55, 54, 38, 72, 73

40, 66, 88, 54, 70

73, 53, 50, 24, 66

51, 46, 42, 40, 21

Field 2 (Treatment 2)

40, 40, 83, 30, 46

53, 50, 50, 24, 25

24, 22, 43, 54, 30

34, 35, 36, 38, 30

An experiment was conducted to investigate the effect of two treatment T1, T2 on wheat growth. The experiment was carried out in two fields. 40 randomly selected plants were treated(20 with T1 and 20 withT2) in each field. The height of the mature plants were recorded as below (in cms). The interset is to answer the following questions.

1) Do the treatments appear to differ in their effect on the growth?

2) Is growth different in the fields?

3) Does the difference between the treatment differ between two fields?

Field 1 (Treatment 1)

90, 123, 108, 93, 100

108, 47, 105, 94, 123

90, 87, 124, 90, 77

110, 65, 93, 54, 60

Field 2 (Treatment 1)

56, 70, 66, 78, 74

72, 108, 87, 99, 61

98, 50, 53, 78, 76

74, 87, 81, 67, 61

Field 1 ( Treatment 2)

55, 54, 38, 72, 73

40, 66, 88, 54, 70

73, 53, 50, 24, 66

51, 46, 42, 40, 21

Field 2 (Treatment 2)

40, 40, 83, 30, 46

53, 50, 50, 24, 25

24, 22, 43, 54, 30

34, 35, 36, 38, 30

1.     The number of white corpuscles on a slide has a Poisson distribution with mean 4.5.

a.     Find the most likely number of white corpuscles om a slide.

b.     Calculate correct to three decima places the probability of obtaining this number

c.     If such two slides are prepared, what is the probability, correct to three decimals places of obtaining at least two white corpuscles in total on the two slides?

An experiment was conducted to investigate the effect of two treatment T1, T2 on wheat growth. The experiment was carried out in two fields. 40 randomly selected plants were treated(20 with T1 and 20 withT2) in each field. The height of the mature plants were recorded as below (in cms). The interset is to answer the following questions.

1) Do the treatments appear to differ in their effect on the growth?

2) Is growth different in the fields?

3) Does the difference between the treatment differ between two fields?

Field 1 (Treatment 1)

90, 123, 108, 93, 100

108, 47, 105, 94, 123

90, 87, 124, 90, 77

110, 65, 93, 54, 60

Field 2 (Treatment 1)

56, 70, 66, 78, 74

72, 108, 87, 99, 61

98, 50, 53, 78, 76

74, 87, 81, 67, 61

Field 1 ( Treatment 2)

55, 54, 38, 72, 73

40, 66, 88, 54, 70

73, 53, 50, 24, 66

51, 46, 42, 40, 21

Field 2 (Treatment 2)

40, 40, 83, 30, 46

53, 50, 50, 24, 25

24, 22, 43, 54, 30

34, 35, 36, 38, 30

1. Consider the following data:

36 39 36 35 36 20 19

46 40 42 34 41 36 42

40 38 33 37 22 33 28

38 38 34 37 17 25 38

a. Develop a frequency distribution, relative frequency distribution, and cumulative frequency distribution.

b. Draw a frequency histogram for the frequency distribution in (a). 

in a certain factory producing cycle tyres there is a small chance of 1 in 500 tyres to be defective. the tyres are supplied in lots of 10 . using Poisson distribution, calculate the approximate number of lots containing no defective one defective and two defective tyres respectively in consignment of 10,000 lots