A population has mean μ = 16 and standard deviation σ = 1.5. A random sample...

A population has mean μ = 16 and standard deviation σ = 1.5. A random sample of size n = 49 is selected. What is the probability that the sample mean is greater than 16.8?

I got 3.73 for z-value.

Please help

Solutions

Expert Solution

Population has a mean =16 and standard deviation = 1.5.

Random sample of size n =49

Sample mean follows normal with mean =16 and standard deviation :

probability that the sample mean is greater than 16.8

i.e P( > 16.8) = 1-P(16.8)

Z -score for 16.8 = (16.8 - 16)/0.2143 = 3.73

From standard normal tables;

P(Z3.73) = 1.000

Generally Standard normal tables are available from -3.5 to 3.5

Any Z Value beyond 3.5 can be taken as 1.0

Also using Excel function : NORM.S.DIST(3.73,1) the value of P(Z3.73) = 0.9999

P(16.8) = P(Z3.73) =1.0

P( > 16.8) = 1-P(16.8) = 1-1.0 = 0

orchestra answered 1 year ago

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