# a) Calculate the mean, median, mode, first quartile and third quartile.

01 / 10 / 2021 Statistics

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QUESTION 1

The daily sales at a food store (sample) :

\$1,520,  \$2,620, \$3,360, \$3,550, \$1,350, \$2,545, \$1,430, \$2,400, \$3,580, \$2,390, \$1,525, \$2,400, \$1,420, \$1,550, \$2,390, \$1,560, \$1,680, \$2,330

a) Calculate the mean, median, mode, first quartile and third quartile.

b) Calculate the range, IQR, variance, standard deviation and Coefficient of variation.

c) What conclusion can you reach about the daily sales at this store?

QUESTION 2

Given the following contingency table:

BST

A 10 15 5

A’ 25 35 10

Where A = Accountancy student,   B = Basketball player,     S=Swimmer,     T=Tennis player

What is the probability of:

a) Marginal Probability of non- Accountancy student?

b) Marginal Probability of Swimmer?

c) Given that a randomly selected student is a Accountancy student, calculate the probability he is either a tennis player or a swimmer.

d) Is the module (Accountancy) independent or dependent of the sports activities?

QUESTION 3

There are 6000 University full-time students.  40% of the students joined students clubs such as Badminton or China students club.    Random samples of 100 customers are selected.

(i) Determine the population mean and Standard Error of all possible sample proportions.

(ii) 80% of the sample proportions symmetrically around the population proportion will have between X% and Y% of Kaplan’s students who joined at least a student’s club.  Compute the value of X and Y.

QUESTION 4

A student taking a MCQ exam with five questions in which each question has four options selects the answers randomly.  What is the probability that the student will get:

a) Five questions correct?

b) At least four questions correct?

c) No questions correct?

d) No more than two questions correct?

QUESTION 5

Assume a Poisson Distribution.

a. If λ=2, Find P(X≥2)

b. If λ=8, Find P(X≥3)

c. If λ=0.5, Find P(X≤1)

d. If λ=4, Find P(X≥1)

e. If λ=5, Find P(X≤3)

QUESTION 6

The quality control manager of XYZ Bakery is inspecting a batch of chocolate biscuits that has just been baked.  If the production process is in control, the mean number of chip parts per biscuit is 6.0.  What is the probability that, in any particular biscuit being inspected,

a) Fewer than five chip parts will be found?

b) Exactly five chip parts will be found?

c) Five or more chip parts will be found?

d) Either four or five chip parts will be found?

e) The variance

QUESTION 7

A toll-free phone number is available from 9am to 9pm for customers to register a complaint about a product purchased from a large company.  Past history indicates that an average of 0.4 calls is received per minute.

a) What properties must be true about the situation described above in order to use the Poisson distribution to calculate probabilities concerning the number of phone calls received in a 1-minute period?

b) Zero phone calls will be received?

c) Three or more phone calls will be received?

d) What is the maximum number of phone calls that will be received in a 1-minute period 99.99% of the time?

QUESTION 8

Briefly describe the meaning of

a) Standard normal distribution and t-distribution.

b) Standard deviation and standard error of the mean.

c) Type I and Type II error.

d) Standard deviation and standard error of the Mean

e) Sampling Distribution

f) Central Limit Theorem

g) Correlation Coefficient

h) Margin of Error

QUESTION 9

What is the impact on the sample size to obtain a 90% confidence interval in estimating the percentage of qualified voters who will support a political candidate, if the margin of error is half of the original?

QUESTION 10

A set of final examination marks in an Engineering  unit is normally distributed with a mean of 70 and a standard deviation of 6.

a. What is the probability that a student obtains a mark between 65 and 79?

b. If the lecturer gives Distinction and High Distinction grades to the top 10% of students, what mark does a student need to get a distinction?

c. If the lecturer gives grades of high distinction to the top 5% of students, are you better off with a mark of 78 on this exam or a mark of 68 on a different exam where the mean is 62 and the standard deviation is 3?  Show your answer statistically and explain.

QUESTION 11

On average, there is a fatal car accidents  occur every 2 days in a town of Malangoro. If it follows exponential distribution,  find the probability that the time between 2 fatal accidents is

a) Less than 3 days

b) More than 1 day

c) Between 1 and 3 days.

QUESTION 12

A poll was conducted by SPP in Aljunate-Mcfersan GRC to find how many will support them in the coming election.  A pilot test shows that 30% of the 2,000 staff interviewed said they would be supporting SPP.

If a new poll is going to be conducted, what is the needed sample size to obtain a 90% confidence interval estimate of the percentage of “support” vote  to within ±10% if you do not have the information on the 30% in the poll who said that they would support SPP?

QUESTION 13

A consumer’s spending is widely believed to be a function of their income.  A university professor tries to estimate this relationship by measuring his students’ spending and income pattern.

Spending(\$) Income (\$)

154 305

135 150

95 100

29 30

124 150

130 175

30 50

73 120

81 122

221 300

132 152

100 125

55 70

94 100

217 220

200 240

224 250

127 150

87 50

a. Construct a scatter diagram

b. State the hypothesis statement for the coefficient of the independent variables

c. Assuming a linear relationship, use the least-square method to find the regression equation.

d. Interpret the meaning of the coefficient of the slope, b.

e. Predict the mean spending for a student with a weekly income of \$225.

f. Compute the correlation coefficient.  Comment on the relationship.

QUESTION 14

The Dean of a business faculty wishes to form an executive committee of five from among the 40 tenured faculty members.  The selection is to be random, and there are eight tenured faculty members in accounting.  What is the probability that the committee will contain

a) None of them?

b) At least one of them?

c) Not more than one of them?

d) What is your answer to (a) if the committee consists of seven members?

QUESTION 15

The Programme Development Department of Mediaworks Production, a film producing company targeting at Asia markets, is considering marketing a new film in 2017.  In the past, 40% of the film released by the company had been successful and 60% had been unsuccessful.  Before introducing a programme to the Asia market, a market study is typically conducted to ascertain the movie’s popularity in Asia. From past record, 40% of successful programme had received a favourable market research report and 30% of the unsuccessful film had received a favourable report.  For the new film under consideration, the findings of the research indicate a favourable report.

(i) What is the probability that the program will be successful, given this favourable report?

(ii) What is the probability that the program will be unsuccessful, given this favourable report?

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