Question

Using Central Limit Theorem) Let S₁₀ sum of 10 Poisson random variables each with mean = 1

1. Find P(S ₁₀ > 10) exactly using Minitab CDF command (Poisson mean =10).

2. Approximate above probability using bell curve approximation -- Normal mean = 0 and standard deviation 1.

3. Show Minitab Command line output

Answer 1

1)

P(S10 > 10)

= 1 - P(S10 <= 10)

=1- 0.583040

= 0.41696

2)

E(X) = 1

sd (X) = sqrt(1) = 1

E(S10) = 10

sd(S10) = sqrt(10) = 3.1622776

P(S10 > 10)

= P(S10 >= 10.5) {continuity correction }

= P(Z > (10.5 - 10)/3.1622776)

= P(Z > 0.158113 )

= 0.4372