Question

6. (Sec. 5.4) Let X denote the price for a randomly selected bouquet of 10 tulips. Suppose the mean value of X is $17.50 and the standard deviation of X is $6.00. (a) Is it plausible that X is normally distributed? Explain why or why not. (b) For a random sample of 55 such bouquets, what is the approximate probability that the sample mean bouquet cost is between $15.00 and $25.00? (c) For a random sample of 55 such bouquets, what is the approximate probability that the total cost is greater than $1100? (d) Could the probabilities in the previous two parts be calculated with reasonable accuracy if the sample size were 18? Explain your reasoning.

Answer 1

Huis There is no Information about dismibution. and Sample size is 10, which is lesser than 30 (CLT). so we can not use normal dis hibution, n> 30 , so CLT can be used and we lam assume that NNCHET;) Where Mx = 17.50 & Z-FM PC15 < X < 25) = P (15-17.5 , 25-17.5 l 6/155 61155

IPC -3.09 <2< 9.27) = P(Z < 9.27) - PC25-3.09) E I- 0.0010 - 0.9990 © * = 1100 = 20 - 1100 55 - 20 P ( X > 202 =Piz> 20-17.5 l $165 ) = P(Z >3.09) = 0.00107 @ No, because n<30 ie only 18 so, wo com not apply CLT.