Question 1 Probability and Probability distributions (22 Marks)

[Spend around 40 minutes to answer this question]

Part A [1+3+3 =7 marks]

The personnel department of Ministry of Education has compiled data on promotion of

secondary school teachers, classified by gender.

Teacher Promoted Not promoted Total

Male 23 92 115

Female 4 16 20

total 27 108 135

a) What is the probability that a male teacher is promoted? [ 3 marks]

b) Given that a teacher is not promoted, what is the probability that teacher is a female. [ 3

marks]

c) Are promotion and gender dependent on each another? Justify. [ 3 marks]

Part B [2+3+1 =6 marks]

Based on past records, Sixty percent of the people entering Damodar City complex in Suva make

a purchase. A random sample of 10 individuals who entered damodar city complex was taken.

i) Define your random variable and justify its probability distribution. [ 2 marks]

ii) What is the probability that more than 8 people out of 10 will make a purchase? [ 3

marks]

iii) On average how many will make purchase if 500 people visit the complex. [ 1 mark]

Part C [4+5= 9 marks]

1) The recent average starting salary for new USP graduates is $20000. Assume that salaries are

normally distributed, with a standard deviation of $4000.What is the cut-off for the bottom

20% of the salaries? [show all workings with diagrams] [ 4 marks]

2) The Puma Company's brand has a market share of 30%. In a survey, 1 000 consumers were

asked which brand they prefer. What is the probability that more than 40% of the

respondents say they prefer the Puma brand?