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 ?.? 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 ? d) Calculate s2 e) Calculate s 1) Assuming the Graduate Management Administration Test (GMAT)

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?