Suppose x has a distribution with = 10 and = 8. (a) If a random sample of size n

Question

Suppose x has a distribution with = 10 and = 8. (a) If a random sample of size n = 33 is drawn, find x, x and P(10 x 12). (Round x to two decimal places and the probability to four decimal places.) x = x = P(10 x 12) = (b) If a random sample of size n = 75 is drawn, find x, x and P(10 x 12). (Round x to two decimal places and the probability to four decimal places.) x = x = 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 part (a) because of the sample size. Therefore, the distribution about x is .

Explanation / Answer

a) here x=10

x =std deviation/(n)1/2 =1.3926

P(10<X<12) =P((10-10)/1.3926<Z<(12-10)/1.3926) =P(0<Z<1.4361)=0.9245-0.5=0.4245

b)

x=10

x =std deviation/(n)1/2 =0.9238

P(10<X<12) =P((10-10)/1.3926<Z<(12-10)/0.9238) =P(0<Z<2.165)=0.9848-0.5=0.4848

c)The standard deviation of part (b) is less then part (a) because of increase of sample size

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