Suppose the birth weight of a live baby lion has a mean of 1500 grams with a sta

Question

Suppose the birth weight of a live baby lion has a mean of 1500 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

a) What theorem will let us treat T and M as normal random variables?  

b) What is the expected value of T in grams?  

c) What is the standard deviation of T?  

d) What is the approximate probability that total weight of the 36 cubs is less than 53000 grams?   

e) What is the standard deviation of M?  

f) What is the approximate probability M is between 1425 and 1575 grams?  

g) What is the probability that M is within 1 standard deviation of its expected value?

Explanation / Answer

a) central limit theorum

b)  expected value of T in grams =1500*36=54000

c) standard deviation of T =300*(36)1/2 =1800

d)approximate probability that total weight of the 36 cubs is less than 53000 grams=P(X<53000)

=P(Z<(53000-54000)/1800)=P(Z<-0.5556)=0.2893

e) standard deviation of M =300/(36)1/2 =50

f)  approximate probability M is between 1425 and 1575 grams=P(1425<X<1575)

=P((1425-1500)/50<Z<(1575-1500)/50)=P(-1.5<Z<1.5)=0.9332-0.0668 =0.8664

g) probability that M is within 1 standard deviation of its expected value=P(-1<Z<1)=0.8413-0.1587 =0.6827

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