Question

3. (a) Outline four (4) characteristics of the normal distribution.

b. The marks scored by the candidates in an examination are normally distributed with mean 54 and standard deviation 16 marks. If the top 12% of the candidates obtained distinction and the bottom 15% failed estimate correct to 2 significant figures:

1) the pass mark

(ii) the least mark for distinction

(C) Suppose that one in five customers buy product Y. If four customers are chosen at random: what is the probability that none of them buy product Y?

(1) what is the probability that at least three of them buy product Y?

(d) The average number of blemishes per painted panel is two. Find the probability that any given panel will contain three or more blemishes.

Answer 1

3a) Four characterstics of the normal distribution: 1. The normal cune is bell shaped and symm- etric about the mean. 2. The mean, median and mode are equal 3. The total area under curve is equal tol 4. The normal curve has an important property that it is asymptotic to the X axis It means the curve extends continuously on either side. As the distance from meam increases, the curve goes nearer to the X axis but does not touch the xaxis. D The marks scored by the candidates in an exam are normally distributed with mean (M) = 54, S.D(G) = 16.

The pass mark te The bottom 15% students are failed. 15% 14G=W Х Let x be the pass mark. Corresponding to 15% =0.15, we get Z value =-1.03645 F By using Quick z. some online calculator We have z= Xu 03643= X-54 16 > X =37.42 i pass mark =37.42 trs (2) The least mark for distinction, Top 12% Students got distinction. Top 12% 887 M=54 x Let x be the least mark of distinction de top 12%.