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Alissa Hutchinson

Alissa Hutchinson

Answered question

2022-04-07

Let Y 1 , Y 2 , . . . , Y n be random samples from a normal distribution where the mean is 2 and the variance is 4. How large must n be in order that P ( 1.9 Y ¯ 2.1 ) 0.99?

My attemp^
We are computing for the sample mean of our random sample that was given in the problem. By definition, z = Y ¯ μ σ n . So rewrite the equation so we can transform the data to make the mean 0 and the standard deviation 1. If I do that, I get,

P ( 1.9 2 2 n z 2.1 2 2 n ) 0.99. This means that

P ( 0.1 2 n z 0.1 2 n ) 0.99. This also means that

P ( 0.05 n z 0.05 n ) 0.99. I am not really sure what to do after this step. I am trying to use the definition of the normal distribution, however that was too difficult to do.

Do you guys know what to do after this step?

Answer & Explanation

Braxton Gallagher

Braxton Gallagher

Beginner2022-04-08Added 21 answers

You just have to set
0.05 n Φ 1 ( 0.995 )
and solve for n

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