The following table was constructed from data collected in a recent Stat 1060 cl

Question

The following table was constructed from data collected in a recent Stat 1060 class. Each student provided information on his or her family. The table gives the number of children in the family, and the height of the father. We defined short fathers to be less than or equal to 66.5 in. tall, middle fathers to be greater than 66.5 and less than or equal to 70.5 in. tall, and tall fathers to be greater than 70.5 in. tall.

Father's ht. No. children

1

2

3

4 or more

Short

2

9

7

6

Middle

8

45

19

8

Tall

4

29

22

14

a) What is the probability that a student chosen at random from the class has a tall father?

b) What is the probability that a student chosen at random from the class comes from a family with at most 3 children?

c) What is the probability that a student chosen at random from the class comes from a family with a short father and 3 children?

Father's ht. No. children

1

2

3

4 or more

Short

2

9

7

6

Middle

8

45

19

8

Tall

4

29

22

14

Explanation / Answer

Following is the completed table:

(a)

Out of 173 students 69 has tall father so we have

P(tall father) = 69 /173 = 0.3988

(b)

That is we need students that comes from family that have either 1 or 2 or 3 children. So number of students comes from family that have atmost 3 children is

15+85+51 = 151

So required probability is

P(at most 3 chidren) = 151 / 173 = 0.8728

(c)

There are 7 students that comes from a family with a short father and 3 children so

P(short father and 3 children) = 7 /173 = 0.0405

Father's ht. / No. children 1 2 3 4 or more Total Short 2 9 7 6 24 Middle 8 45 19 8 80 Tall 4 29 22 14 69 Total 15 85 51 28 173

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