Suppose x has a distribution with μ = 12 and σ = 5. (a) If a random sample of size n = 43 is drawn, find μ x , σ x and P (12 ≤ x ≤ 14). (Round σ x to two decimal places and the probability to four...

(a) If a random sample of sizen = 43 is drawn, find μ_x, σ _x andP(12 ≤ x ≤ 14). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(12 ≤ x ≤ 14) =

(b) If a random sample of sizen = 74 is drawn, find μ_x, σ _x andP(12 ≤ x ≤ 14). (Round σ _x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(12 ≤ x ≤ 14) =

(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  ---Select--- smaller than  or the same as or  than part (a) because of the  ---Select--- smaller or same or larger sample size. Therefore, the distribution about μ_x
is  ---Select--- narrower or the same or wider .