FORMATIVE Q.1

1. Suppose the following table gives the selling prices in tens of thousands of dollars for 20 different homes sold during a month

60.5	113.5	79.0	475.5
75.0	70.0	122.5	150.0
100.0	125.5	90.0	175.5
89.0	130.0	111.5	100.0
50.0	340.5	100.0	525.0

a) Find the mode, median and mean of the selling prices of the first two columns

b) Find the range, variance and standard deviation of the selling prices of the first two columns

c) Find the ninety-fifth percentile, the seventh decile, and the first quartile of the selling prices of homes by taking into consideration the whole table of values.

d) Find the percentiles for the selling prices 75.0, 90, 125.5 and 340.5 by taking into consideration the whole table of values.

e) Construct a box plot of the selling prices in the table above by following the instructions below: - First, find the minimum, maximum, first quartile, median and third quartile of the data - Second, draw roughly the box plot showing the location of each value found in the first given instruction above. - Tell from the box plot drawn above if the data is symmetric, left skewed or right skewed.

1. Suppose the following table gives the age distribution of people buying a newly introduced product in the market. a) Find the mode, median and mean

b) Find the range, variance and standard deviation for the distribution

Age	Frequency
20-29	11
30-39	25
40-49	14
50-59	7
60-69	3

FORMATIVE Q.2

1. Suppose the numbers of people who attended the meeting for which they were

invited if they were from region A or region B, and if they were of the ages

between 30 and 40 or between 50 and 70 are given in the following contingency table.

Age Region

A B

Between 30 and 40 20 15

Between 50 and 70 30 25

a) Create the joint probability table for the people who attended the meeting

b) What is the probability that the person who attended the meeting is from region

A?

c) What is the probability that the person who attended the meeting is from region

A and is of the age between 30 and 40?

d) What is the probability that the person who attended the meeting is from region

B or is of the age between 50 and 70?

e) What is the probability that a person who attended the meeting is from region A

or region B?

f) What is the probability that the person who attended the meeting is from region

B if the person is of the age between 50 and 70?

g) What is the probability that the person who attended the meeting is neither from

region B nor of the age between 50 and 70?

2. In a Grade 7 class, we find that of all pupils, 15% love Mathematics, 30% love

English, 20% love Science, and 25% love both Mathematics and English.

a) What is the probability that a pupil loves Mathematics or English?

b) What is the probability that a pupil loves Mathematics if they love English?

c) Is a pupil loving Mathematics independent of loving English? Give the reason.

3. Suppose we are involved in an experiment of observing the sex of the children in

families having three children.

a) Construct a tree diagram showing the sample space of the experiment

b) How many outcomes would we have from the tree diagram constructed in a)?

Prove the answer given by the multiplication technique of counting.

c) What is the probability that

i) At least one of the children is a boy?

ii) None of the children are girls?

iii) All of the children are boys?

iv) All the children are of the same sex?

4. The Bursaries' Committee of a certain country offers scholarships to only 4

students from a particular school who come out first, second, third and fourth in

their final year examinations.

a) Find the number of ordered ways the students can qualify for a scholarship if

the school has 10 students sitting for their final examinations.

b) If out of 10 students that sat for the examinations, 6 were girls, find the

probability that all 4 qualified students in a) above were girls?

5. Solve for exercise 4. Above where order is not important.