Question

Suppose a company runs a promotion at a sporting event. In the promotion one fan has a chance to catch 3 balls and if they catch all balls they get a prize. The probability of catching a ball is 0.76. What is the probability the fan wins the prize?

A sales representative knows that the probability of a client making a purchase is 0.34. The probability of a client placing an inquiry given they are going to make a purchase is 0.83 while the probability of a client placing an inquiry given that they are not going to make a purchase is 0.27. What is the probability of a client making a purchase given that they make an inquiry

You are working with a research team and want to construct a 95% confidence interval for the mean of consumer spending with a margin of error of no more than $10.1. Your team believes that the variance of spending is 993.1. What is the necessary sample size for constructing the confidence interval?

Answer 1

1) probability the fan wins the prize =(0.76)³ =0.4390

2)

probability of a client making a purchase given that they make an inquiry

=0.34*0.83/(0.34*0.83+0.66*0.27)=0.6129

3)

for 95 % CI value of z=	1.960
standard deviation σ=	31.5135
margin of error E =	10.1
required sample size n=(zσ/E)2                                         =	38.0