Introduction to Statistics

  

Q1- Suppose you invest a fixed sum of money in each of five Internet business ventures. Assume you know that 70% of each ventures are successful, the outcomes of the ventures are independent of one another, and the probability distribution for the number, x, of the successful ventures out of five is   

x

0

1

2

3

4

 

P(x)

0.002

0.029

0.132

0.360

0.168

a) Calculate µ. 

b) Calculate variance.

c) Calculate standard deviation.

Q2- If x is a binomial random variable, compute p(x) for the following 

case: n= 6, p = 0.37 Find the following probabilities:

a) p(x= 2)

b) p(x>4)

c)p(x≤ 3)

c) Calculate µ

d) Calculate s2

e) Calculate s

1) Assuming the Graduate Management Administration Test (GMAT) scores are normally distributed with mean 500, and standard deviation 100 . find the following probabilities: 

a) What proportion falls between 500 and 550? 

b) What proportion falls between 450 and 600? 

c) What proportion falls between 550 and 750?