Question

The raw data has been organised in the frequency table below.

games frequency

6 2

7 5

8 n

9 4

10 4

11 2

12 2

13 2

(a) Write down the value of n.

(b) Calculate the mean number of games played per set.

(c) What percentage of the sets had more than 10 games?

(d) What is the modal number of games?

Answer 1

Answer (a):

Value of n = 4

Answer (b):

The mean number of games played per set is:

$\bar{x}=\frac{\Sigma fx}{\Sigma f}$

$\bar{x}=\frac{227}{25}=9.08$

Answer (c):

Percentage of the sets had more than 10 games is:

$P(X>10)=P(Z>\frac{\bar{x}-\mu}{\sigma})$

$P(X>10)=P(Z>\frac{10-9.08}{2.04})$

$P(X>10)=P(Z>0.45)$

Using normal distribution table, the probability in respect to Z score is 0.6736.

$P(X>10)=1-P(Z<0.45)=1-0.6736$

$P(X>10)=0.3264$

Answer(d):

The modal number of games is 7 because its frequency is 5 which is greatest among all games.