QUESTION 1:

The data is arranged until column 66

Find mean, median, mode, range, variance and standard deviation.

For question 1(a). we use the function in microsoft excel.

1(a) : By using the function in Microsoft excel, we can find the :-

Mean = 26.212

Median = 27

Mode = 28

Range = 84

Variance = 115.46200

Standard Deviation = 10.74532

This is the instruction to get all the following 1(a) answer :

Mean: Enter the following formula, without quotes, to find the arithmetic mean of your set of numbers: "=AVERAGE(A1:A66)". Press "Enter" to complete the formula and the mean of your numbers will appear in the cell.

Median: Enter the following formula, without quotes, into the cell: "=MEDIAN(A1:A66)". Press "Enter" and the median of your set of numbers will appear in the cell.

Mode: Enter the following formula, without quotes, into the cell: "=MODE.MULT(A1:A66)". Press "Enter" and the cell will display mode of the data set.

Range: Enter the following formula, without quotes, into the cell: "=MAX(A1:A66)-MIN(A1:A66)". Press "Enter" and the cell will display the range for your set of data.

Variance:The formula “=VAR.S(A1:A66)”

Standard Deviation: Enter the following formula “=STDEV.S(A1:A66)” and press the enter key to complete the entry.

b) Histogram

In case of omitting the outliers from the data:

a) Find mean,median,mode,range,variance and standard deviation.

In this question, the number -2 and -44 is ignored and deleted in the Microsoft excel to obtain the answer. We use same step to find all :

Mean = 27.75

Median = 27.5

Mode = 28

Range = 24

Variance = 25.84127

Standard Deviation = 5.083431

Draw a histogram using the class width 5

b) The type of distribution is normal distribution

C) The value of skewness was obtained from the Microsoft excel.

The answer display in column A67 in Microsoft excel. Therefore the value of skewness is 0.15417.

e) Find the probability that the light travels with speed

1) Greater than 20

By using the Microsoft excel we can get the value for p(x<20).

P(x<20) = 0.06368

So for p(x>20) = 1 - P(x<20) = 0.06368

= 1- 0.06368

= 0.93632

2) Between 20 to 30

By using Microsoft excel, the p(x<30)

p(x < 30) = 0.67098

p(20 < x > 30) = 0.67098 - 0.06368

= 0.6073

3) less than 20

p(x < 20) = 0.06368

QUESTION 2 :

n = 20 , p = 0.1 , q = 0.9

P(X3) = P(X=0) + P(X=1) + P(X=3)

xnxqpxnxp )()(

The probability is 0.8670.