Question

Can someone help from e-j please thanks.

The mean weight of a face pumpkin (used for carving) being sold at Manning Farm is 15 pounds with a standard deviation of 3 pounds. The mean weight of a face pumpkin (used for carving) being sold at Irving Farm is 17 pounds with a standard deviation of 4 pounds. It is known that pumpkin weights are normally distributed. Dylan must buy some pumpkins for the school Pumpkin Fair. Suppose he randomly selects 8 face pumpkins from the Manning Farm with weights X1,X2..Xg Independently, he randomly selects 7 pumpkins from the Irving Farm with weights Y1,Y2..Y Let Xbar be the mean of the Manning weights and let Xsum be the sum of the Manning weights. Let Ybar be the mean of the Irving weights and let Ysum be the sum of the Irving weights. Let Tbar Xbar-Ybar Let Tdif- Xsum Ysum. Let Tsum-xsum +Ysum a) What is the probability that X1 is no more than 14 pounds? .3695 b) What is the standard deviation of Xbar? 10607 c) What is the probability that Xbar is no more than 14 pounds? 0.1729 d) What is the standard deviation of Xsum? 8.4853 e) Suppose Tbar = Xbar-Ybar? what is the standard deviation of the random variable Tbar? f) What is the expected value of Tbar? g) What is the probability that Tbar > 0 h) What is the standard deviation of the random variable Xsum - Ysum? i) What is the probability that Xsum - Ysum >0? j) If our 15 pumpkins weigh at least 250 pounds in total, then we win the PPP prize. What is the probability that we win the PPP prize?

Answer 1