Estimate a defect probability from a frequency table

A company manufactures a wide variety of components for use in domestic appliances.

The company introduces a new type of light fitting for refrigerators. Each day a supervisor selects a sample of 100 of the light fittings for testing.

(i) How should the light fittings be selected? Give a reason for this method of selection.

The supervisor records the number of faulty light fittings found on each of 150 working days. Her results are shown in the table.

Number faulty	Number of days
0	4
1	19
2	38
3	41
4	22
5	16
6	6
7	4
8 or more	0

(ii) Use the information in the table to estimate $p$, the probability that a light fitting is faulty.

(iii) Assuming the number of faulty fittings found each day follows the binomial distribution $B(100,p)$, find the expected number of days on which 3 faulty fittings are found in a period of 150 working days.