Question

In: Statistics and Probability

Topic: Linear combination of random variables Let X1, X2, . . . , X16 be 16...

Topic: Linear combination of random variables

Let X1, X2, . . . , X16 be 16 independent variables identically distributed as N(2, 4), with an average X̄(Note: This is X bar, It was formatted as X¯ before but I assumed X̄ is more clear in text ) . Find the value c for which P(2 − c ≤ X̄ ≤ 2 + c) = 0.99.

Please show work and relevant formula's

Thanks.

Expert Solution

X1, X2, . . . , X16 be 16 independent variables identically distributed as N(2, 4), with an average X̄

Here Xi ~ N(2,4)

Mean = 2

Variance = 4

Now

So

According to question

using symmetry

Using normal table distribution

c=2.58/2 = 1.29

C =1.29 answer

orchestra answered 2 years ago

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