Question

Solve the question below and show all steps: In a random sample of 28 female students at a college, it was discovered that each of them possessed multiple hand bags. The number of hand bags possessed by each of the 28 female students is listed as follows: 4 4 3 3 3 6 4 2 2 2 1 3 3 3 3 4 4 3 2 8 2 2 3 4 3 3 4 2

a. Find the mean and standard deviation for the sample data set.

b. Form the interval, ?̅±2s

c. According to Chebychev’s rule, what proportion of sample observations will fall within the interval in part b?

d. According to the Empirical Rule, what proportion of sample observations will fall within the interval in part b?

e. Determine the actual proportion of sample observations that fall within the interval in part b. Does the Empirical Rule provide a good estimate of the proportion?

Answer 1

a)

Mean of data set is given as

Standard deviation of data set is given as

Calculations are shown in below table

Data (X)	Mean	X-mean	(X-mean)^2
4	3.214	0.786	0.617796
4	3.214	0.786	0.617796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
6	3.214	2.786	7.761796
4	3.214	0.786	0.617796
2	3.214	-1.214	1.473796
2	3.214	-1.214	1.473796
2	3.214	-1.214	1.473796
1	3.214	-2.214	4.901796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
4	3.214	0.786	0.617796
4	3.214	0.786	0.617796
3	3.214	-0.214	0.045796
2	3.214	-1.214	1.473796
8	3.214	4.786	22.9058
2	3.214	-1.214	1.473796
2	3.214	-1.214	1.473796
3	3.214	-0.214	0.045796
4	3.214	0.786	0.617796
3	3.214	-0.214	0.045796
3	3.214	-0.214	0.045796
4	3.214	0.786	0.617796
2	3.214	-1.214	1.473796
N-1	27	Total	50.71
		S.D	1.3704

b)

Interval for

Interval is given as{0.473,5.954}

c)

We have to find what proportion of sample observations will fall within the interval in part b according to chebchyev's rule

According to chebyshev's rule At least 75% measurement will fall with in two standard deviations

d)

We have to find what proportion of sample observations will fall within the interval in part b according to emiprical rule

Expected proportion using empirical rule will be approximately 95% of measurements will fall with in two standard deviations

e)

Total data points fall with in interval are 26 out of 28

Actual proportion which fall with in the interval is

=26/28*100=92.85%

Yes empirical rule provide a good estimate of the proportion