6. 0.34/1 points 1 Previous Answers Suppose x has a distribution with ? = 24 and

Question

6. 0.34/1 points 1 Previous Answers Suppose x has a distribution with ? = 24 and ? t12 6.5 011 Notes O Ask Your T 20 (a) If a random sample of size n-32 is drawn, find AG. ?i and p(24 S x S 26). (Round o, to two decimal places and the probability to four decimal places.) 24 si s 26) and P(24 x S 26). (Round ? to two decimal places (b) If a random sample of size n . 65 is drawn, find ?. ? and the probability to four decimal places.) (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 smaller thanpart (a) because of the largersample size. Therefore, the distribution about is narrower Need Help?

Explanation / Answer

Solution :

Given that ? = 24 , ? = 20

(a) Given that n = 32

?x-bar = 24

?x-bar = ?/sqrt(n) = 20/sqrt(32) = 3.54

P(24 <= x-bar <= 26) = P((x - ?x-bar)/?x-bar <= Z <= (x - ?x-bar)/?x-bar)

= P((24 - 24)/3.54 <= Z <= (26 - 24)/3.54)

= P(0 <= Z <= 0.5650)

= 0.2157

(b) Given that n = 65

?x-bar = 24

?x-bar = ?/sqrt(n) = 20/sqrt(65) = 2.48

P(24 <= x-bar <= 26) = P((x - ?x-bar)/?x-bar <= Z <= (x - ?x-bar)/?x-bar)

= P((24 - 24)/2.48 <= Z <= (26 - 24)/2.48)

= P(0 <= Z <= 0.8065)

= 0.2910

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