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given normal random variable x with mean μ= 57.1 and standard deviation σ=13.2, what is P...

given normal random variable x with mean μ= 57.1 and standard deviation σ=13.2, what is P (46 < x̄ < 69) for a sample of size n= 16?

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Answer #1

Solution :

= / n = 13.2 / 16 = 3.3

= P[(46 - 57.1) / 3.3< ( - ) / < (69 - 57.1) / 3.3)]

= P(-3.36 < Z < 3.61)

= P(Z < 3.61) - P(Z < -3.36)

= 0.9998 - 0.0004

= 0.9994

P(46 < < 69) = 0.9994

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