In: Statistics and Probability
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
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 |
|
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 |
|
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