Question

Suppose x has a distribution with μ = 10 and σ = 7.

(a) If a random sample of size n = 40 is drawn, find μ_x, σ _x and P(10 ≤ x ≤ 12). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(10 ≤ x ≤ 12) =

(b) If a random sample of size n = 63 is drawn, find μ_x, σ _x and P(10 ≤ x ≤ 12). (Round σ _x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(10 ≤ x ≤ 12) =

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is larger than / the same as / smaller than part (a) because of the smaller / same / larger sample size. Therefore, the distribution about μ_x is wider / the same / narrower.

Answer 1

solution Gives el = 10 6 = 7 a) D:40 e x = 10 P (losxs12) = PC 10-10 < x- el x < 12-10 .11 6x = P( 525 22 ) =P(0323 1.80) = P(Z< 1.80) - P(240) = 0.9641-0.5 = 0.464 1 e x = 10 6x = lol p(10<x512) = 0.4641

b) n = 63 el x = 10 6xCo - More - 0.88 p(105x512) =P(10-10 X-el x x 12-101 0.88 6x 0.88 2. 0.88525 ose) = poszs 2.27) = P(ZC 2.27) - P(ZLO). = 0.9884-0.5 = 0.4884 ex=110 6x=0.88 P(10<x< 12) = 0.4884) c) The probability of part b' to be higher thon that part of part ol. The standard deviation of part b is smaller than port à becouse of не ол е sample size. Thеѕе fате ме distribution abcut lex is the some