Question

A random sample of 100 observations Denote byX1,X2,...,X100, were selected from a population with a mean μ= 40 and variance σ2= 400.

Determine P(38< ̄X <43), where ̄X= (X1+X2+...+X100)/100.

Answer 1

This is a normal distribution question with

Sample size (n) = 100

Since we know that

P(38.0 < x < 43.0)=?

This implies that

P(38.0 < x < 43.0) = P(-1.0 < z < 1.5) = P(Z < 1.5) - P(Z < -1.0)

P(38.0 < x < 43.0) = 0.9331927987311419 - 0.15865525393145707

PS: you have to refer z score table to find the final probabilities.

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