Question

Jack is a quality control engineer for a large electronic company. Her job is to thoroughly test each stereo set manufactured by the company and to classify it as acceptable or unacceptable. Due to the company’s rigorous quality standards, each set has an equally likely chance of being acceptable or unacceptable. On a Monday morning, Felicia inspects six (6) sets. Find the probability that she

(i). Rejects all the sets.

(ii). Accepts all the sets.

(iii). Accepts at least three of the sets.

(iv). Rejects at most four of the sets.

(b). If Jack inspected 10 stereos on a Tuesday morning,

(i). What is the expected number of stereos to inspect.

(ii). What is the standard deviation of the number of stereos to be inspected.

(iii). What is the difference between the expected number of stereos on Tuesday and Monday.

Answer 1

Question 1:

The distribution given here for the number of sets rejected is modelled as:

a) The required probability here is computed as:

b) The required probability here is computed as:

c) The required probability here is computed as:

Accepts at least 3 sets = Same as reject at most 3 sets

d) The probability here is computed as:

(b) For 10 radios, the distribution of rejected ones become:

(i) Expected number of stereos to inspect to be rejected = np = 10*0.5 = 5

(ii) Standard deviation is computed as:

(iii) The difference in the expected number of stereos on Tuesday and monday is computed as:

= 0.5*(10 - 6) = 2

Therefore 2 is the required difference here.