Question

Suppose an x distribution has mean μ = 2. Consider two corresponding  x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.

(a) What is the value of the mean of each of the two x distributions?

For n = 49, μ_x=

For n = 81, μx=

Suppose x has a distribution with μ = 54 and σ = 5.

Find P(50 ≤ x ≤ 55). (Round your answer to four decimal places.)

Answer 1

For n = 49, = 54

For n = 81, = 54

P(50 < < 55)

= P((50 - )/() < ( - )/() < (55 - )/())

= P((50 - 54)/(5/) < Z < (55 - 54)/(5/))

= P(-5.6 < Z < 1.8)

= P(Z < 1.8) - P(Z < -5.6)

= 0.9641 - 0

= 0.9641