Let X_{1}, X_{2},...,X_{n} be n independent random variables each with mea

Dolly Robinson

Dolly Robinson

Answered question

2021-10-23

Let X1,X2,,Xn 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(X>2000)0.95.

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-10-24Added 95 answers

Step 1
Given that μ=100 and σ=30
E(X)=E(Xi)=nμ=100n
σ(X)=σ(Xi)=30{n}
Step 2
Consider,
P(X>2000)0.95
P(XE(X)σ(X)>2000100n30{n})0.95
P(z>20010n3{n})0.95
1P(z20010n3{n})0.95
10.95P(z20010n3{n})
P(z20010n3{n})0.05
20010n3{n}1.645
20010n4.935n
4.935n10n+2000
n4.23
n=17.89
18
Thus, n=18.

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