Suppose x has a distribution with a mean of 60...

Question

Suppose x has a distribution with a mean of 60 and a standard deviation of 27. Random sample of size n=36 are drawn.

(a) Describe X distribution.

compute the mean and standard deviation of the distribution.¦

µ‾x=

σ‾x=

Find the z value corresponding to‾x=51

=

find P(‾x<51). ( enter a number. Round your answer to four decimal places.)

Answer 1

From the CLT, if the population distribution is normal, the sample distribution is normal, and if the distribution is non-normal, as the sample size increases, the distribution approaches the normal.

The mean of a sample is the same as the population mean. However, the standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size.

Thus, µ_x-bar = 60

σ_x-bar = 27/√36 = 27/6 = 9/2

z = (51 - 60)/(9/2) = -9/(9/2) = -2

P(x-bar <= 51) = Φ(-2) = .0228