Question

The number of breakdowns each day on a section of road were recorded for a sample of 250 days

as follows:

Number of breakdowns Number of days

0 100

1 70

2 45

3 20

4 10

250

Calculate the 95 per cent and the 99 per cent confidence intervals for the mean. Explain your

results.

Answer 1

We have, E(X) = [(0 * 100) + (1 * 70) + (2 * 45) + (3 * 20) +

(4 * 10)]/(100 + 70 + 45 + 20 + 10) = 1.04.

E() = [(0 * 100) + (1 * 70) + (4 * 45) + (9 * 20) +

(16 * 100)]/(100 + 70 + 45 + 20 + 10) = 8.12.

Var(X) = E() - (X) = 8.12 - 1.0816 = 7.0384.

s.d.(X) = 2.6530.

95% C.I. for mean of the population is:

[, ], where, = 1.04, s = 2.6530,

n = 250, = 1.97;

= [1.04 - 0.3305, 1.04 + 0.3305] = [0.7095, 1.3705]. (Ans).

Interpretation of 95% C.I. : We are 95% confident that the

population mean will lie within the above confidence

interval. (Ans).

99% C.I. for mean of the population is:

[, ], where, = 2.596;

= [1.04 - 0.4356, 1.04 + 0.4356] = [0.6044, 1.4756]. (Ans).

We are 99% confident that the population mean will lie

within the above confidence interval. (Ans).