# (Statistical probability ...20

Question 1

(a) A study of long-distance mobile phone calls carried out by a local telephone company revealed that the duration of the calls, in minutes, follows the normal probability distribution. The mean duration per call was 4.2 minutes and the standard deviation was 0.6 minutes.

(i) Find the duration of call in d minutes such that 4% of the calls have longer durations than d. (5 marks)

(b) An insurance company classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30%, 50%, and 20%, respectively. The probability a “good” driver will have an accident is 0.01, the probability a “medium” risk driver will have an accident is 0.03, and the probability a “poor” driver will have an accident is 0.1. The company sells Mrs. Cheung an insurance policy.

(ii) According to the insurance company, what is the probability that Mrs. Cheung will have an accident? (4 marks)

### 1 個解答

• 最佳解答

(a) (i)

Let D minutes be the duration, D ~ N(4.2, 0.6²)

Consider Pr(D > d) = 4%

Pr( Z > (d-4.2)/0.6 ) = 4%

(d-4.2)/0.6 = 1.75

d = 5.25

(b) (ii)

30% * 0.01 + 50% * 0.03 + 20% * 0.1 = 0.038 = 3.8%