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given a normal distribution with μ=105 and σ=10, if you select a sample of n=4. There...

given a normal distribution with μ=105 and σ=10, if you select a sample of n=4. There is a 67​% chance that X(mean)is above what​ value? ​(Type an integer or decimal rounded to two decimal places as​ needed.)

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Answer #1

From Z Table, we get probability = 0.67 when z = 0.44

We know that,

z = (X- μ) /(σ/n1/2)) = (X – 105)/(10/2) = (X – 105)/5

So,

X = 105 + 5*0.44 = 107.20

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