Question

1. Your study found that 72% of participants in your study were happy. If you were to interview 20 people, what is the probability that 14 are happy? [4 marks]

2. Your study found that annual income is normally distributed with a mean of 1600 hours and standard deviation of 250 hours. What is the probability that a participant will work at least 1400 hours in a year? [4 marks]

Answer 1

a) Give data :

72% of participants in your study were happy

p=72%=0.72

n=20

X~B(n,p)

Formula:

Prob mass fundtion of binomial distribution is

Where

Calculate :probability that 14 are happy

P(X=14)

b)  mean = 1600 hours

  standard deviation = 250 hours

annual income is normally distributed

Calculate:

probability that a participant will work at least 1400 hours in a year

Using Normal probability table