X₁ , X_{2 ,} X₃ , ....... , X₁₀₀ are i.i.n random variables that have a uniform distribution on the following numbers: [-3 , -2, -1, 1, 2, 3]. X_k take each value an equal probability of 1/6.

a) What is the standard deviation of any X_k k=1 , 2 , ..... , 100?

b) What is the expected value of the sum X₁ , X_{2 ,} X₃ , ....... , X_100, E(S₁₀₀)=______ ?

c) The normal approx. to P(0< S_n< 43.2) is closest to which of the following?

• 0.95
• 0.68
• 0.50
• 0.35