Suppose the birth weight of a live baby lion has a mean of 1490 grams with a sta

Question

Suppose the birth weight of a live baby lion has a mean of 1490 grams with a standard deviation of 300 grams. Let T the total weight of 36 randomly selected lion cubs and let M be the mean of the weights of 36 randomly selected lion cubs. Because the sample size > 30 we can assume approximate normality. a) What is the expected value of T in grams? b) What is the standard deviation of T? c) What is the approximate probability that total weight of the 36 cubs is less than 53000 grams? d) What is the standard deviation of M? e) What is the approximate probability M is between 1425 and 1575 grams?

Explanation / Answer

Ans:

a)Expected value of T=1490*36=53640

b)standard deviation of T=36*300=10800

c)

z=(53000-53640)/10800=0.059

P(z<0.059)=0.5236

d)standard deviation of M=300/sqrt(36)=300/6=50

e)

z(1425)=(1425-1490)/50=-1.3

z(1575)-(1575-1490)/50=1.7

P(-1.3<=z<=1.7)=P(z<=1.7)-P(z<=-1.3)=0.9554-0.0968=0.8586

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