Answer choices for pt c (c) Why should you expect the probability of part (b) to

Question

Answer choices for pt c

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

Suppose x has a distribution with Au 12 and a 36. a) If a random sample of size n 48 is drawn, find AG, a and P 12 s x S 14). Round ax to two decimal places and the probability to four decimal places P012 s x s 14) (b) If a random sample of size n 67 is drawn, find ux, a and P 12 s x S 14). (Round ax to two decimal places and the probability to four decimal places.) P(12 s x s 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 part (a) because of the Selec sample size. Therefore, the distribution about is Select

Explanation / Answer

a)mean = 12

here std error =std deviation/(n)1/2 =0.87

P(12<X<14) =P((12-12)/0.87<Z<(14-12)/0.87)=P(0<Z<2.3094)=0.9895-0.5=0.4895

b)mean =12

std error =std deviation/(n)1/2 =0.73

P(12<X<14) =P((12-12)/0.73<Z<(14-12)/0.73)=P(0<Z<2.7285)=0.9968-0.5=0.4968

c)The standard deviation of part (b) is smaller than part (a) because of thelarger) sample size. Therefore, the distribution about x is narrower

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