**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? **