Question

Suppose x has a distribution with μ = 13 and σ = 7.

(a) If a random sample of size n = 43 is drawn, find μ_x, σ_x and P(13 ≤ x ≤ 15). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(13 ≤ x ≤ 15) =

(b) If a random sample of size n = 58 is drawn, find μ_x, σ_x and P(13 ≤ x ≤ 15). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(13 ≤ x ≤ 15) =

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

Answer 1

c) probability of b) is high than a) because the sample size increase

we know the sample size increases then standard error dicreases

there fore the sample size increases then confidence interval is narrower.