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In: Statistics and Probability

QUESTION ONE The data below represent statistics and probability end of semester examination marks of 30...


QUESTION ONE
The data below represent statistics and probability end of semester examination marks of 30
students randomly selected from the population of students who registered for probability and
statistics during 2018/2019 academic year.
16 51 36 45 23 48
37 19 28 28 25 36
76 22 27 18 28 42
38 47 44 29 37 42
27 33 35 46 28 27
Using sturge’s approximation rule with all your answers in one decimal place,
construct a frequency distribution table as follows
Class
Boundary
Tally Frequency Class
midpoint
CF FX FX^2
Calculate the coefficient of skewness for the data set and interpret our result.

QUESTION TWO
Suppose that the operations manager of a nose mask packaging delivery service is
contemplating the purchase of a new fleet of trucks during this COVID-19 period. When
packages are efficiently stored in the trucks in preparation for delivery, two major constraints
have to be considered. The weight in pounds and volume in cubic feet for each item. Now
suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard
deviation of 3.9 pounds. In addition suppose that the average volume for each of these
packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the
variation of the weight and volume?

QUESTION THREE
The marketing director of GH HOTEL was interested in studying the intention of consumers
to visit their facility after the president has fully lifted the restriction on public gathering in
2020 and as a follow- up, whether they in fact actually visited. Suppose that a sample of 1000
household was initially selected and the respondents were asked whether they planned to visit
GH HOTEL. Twelve months later the same respondents were asked whether they actually
visited the hotel. The results are summarized in the table below
Planned to visit
Actual visit
Yes No Total
Yes 200 50 250
No 100 650 750
Total 300 700 1000
i. Draw a tree diagram to represent the information in the table.
ii. Find the probability of selecting a respondent who actually visited GH HOTEL.
Interpret your answer in a simple single sentence.
iii. Find the probability of panned visit or actual visit.
iv. Calculate the probability that a respondent actually visited GH HOTEL given that he
or she planned to visit GH HOTEL

Solutions

Expert Solution

The table 1 below shows calculation up to

Class Boundary Mid-Point Frequency Tally Frequency
Lower B to Upper Boundary x = (LB + UB)/2 f Cumulative Frequency (CF) fx fx2
10 to 20 15 /// 3 3 45 675
20 to 30 25
//// //// /
11 14 275 6875
30 to 40 35
//// //
7 21 245 8575
40 to 50 45
//// //
7 28 315 14175
50 to 60 55 / 1 29 55 3025
60 to 70 65 0 29 0 0
70 to 80 75 / 1 30 75 5625
1010 38950

Table 2 for calculation of moments and measures of coeefcient of skewness

Class Boundary Mid-Point Frequency
Lower B to Upper Boundary
x = (LB + UB)/2
f fx fx2 fx3
10 to 20 15 3 45 675 10125
20 to 30 25 11 275 6875 171875
30 to 40 35 7 245
8575
300125
40 to 50 45 7 315 14175 637875
50 to 60 55 1 55 3025 166375
60 to 70 65 0 0 0 0
70 to 80 75 1 75 5625 421875
1010 38950 1708250

The coefficient of Skewness is defined by

.... (i)

..... (ii)

First let us caculate the following

Replacing the above values in (ii)

Replacing the value in equation (i) to calculate the coeeficient of skewness

The data set is positively skewed since g1 is positive


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