Question

Suppose x has a distribution with μ = 23 and σ = 17. (a) If a random sample of size n = 46 is drawn, find μx, σ x and P(23 ≤ x ≤ 25). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(23 ≤ x ≤ 25) = (b) If a random sample of size n = 63 is drawn, find μx, σ x and P(23 ≤ x ≤ 25). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(23 ≤ x ≤ 25) =

Answer 1

Solution :

(a)

= / n = 17 / 46 = 2.51

= P[(23 - 23) / 2.51 < ( - ) / < (25 - 23) / 2.51)]

= P(0 < Z < 0.80)

= P(Z < 0.80) - P(Z < 0)

= 0.7881 - 0.5

= 0.2881

P(23 < < 25) = 0.2881

(b)

= / n = 17 / 63 = 2.14

= P[(23 - 23) / 2.14 < ( - ) / < (25 - 23) / 2.14)]

= P(0 < Z < 0.93)

= P(Z < 0.93) - P(Z < 0)

= 0.8238 - 0.5

= 0.3238  

P(23 < < 25) = 0.3238