Question

Suppose x has a distribution with μ = 17 and σ = 12.

(a) If a random sample of size n = 33 is drawn, find μ_x, σ_x and P(17 ≤ x ≤ 19). (Round σ_x to two decimal places and the probability to four decimal places.)

P(17 ≤ x ≤ 19) =

(b) If a random sample of size n = 71 is drawn, find μ_x, σ_x and P(17 ≤ x ≤ 19). (Round σ_x to two decimal places and the probability to four decimal places.)

P(17 ≤ x ≤ 19) =

Answer 1

(a) P(17 ≤ x ≤ 19) = 0.3308

μx = 17

σx = 12 / sqrt(33) = 2.0889

z = (x - μ) / σ

P(Z<17) = (17-17) / 2.0889 = 0

P(z < 19) = (19-17)/2.0889 = 0.9574

P(17 ≤ x ≤ 19) = 0.3308

(b) If a random sample of size n = 71 is drawn, find μx, σ x and P(17 ≤ x ≤ 19). (Round σ x to two decimal places and the probability to four decimal places.)

P(17 ≤ x ≤ 19) =0.4199

μx = 17;

σ x = 12/sqrt(71) = 1.4241

z = (x - μ) / σ

P(Z<17) = (17-17) / 1.4241= 0

P(z < 19) = (19-17)/1.4241= 1.4044

P(17 ≤ x ≤ 19) = 0.4199