Yasmin

Answered

2021-09-03

Let $X}_{1},{X}_{2},\dot{s},{X}_{n$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that Pr$\left(X>2000\right)\ge 0.95$

Answer & Explanation

Faiza Fuller

Expert

2021-09-04Added 108 answers

Step 1

So, Var

Now given that,

So

and

So, Var(X) = 900n

Step 2

By Central Limit Theorem,

Now, P(X>2000)>0,95

implies

implies

implies

Here you can solve this in two methods,

Trial and error method

Numerically using root finding method

Using trial and error method,

For n = 22

For n=23

So, for n = 23 it is crossing -1.645. Hence n = 23

Most Popular Questions