7.+ Question Details My Notes Ask Your Teacher Suppose the birth weight of a liv

Question

7.+ Question Details My Notes Ask Your Teacher 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 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? f) Enter any comments into the text box here

Explanation / Answer

Answer to the question is as follows:

Mean = 1490
Stdev =300
n = 36

a. Expected value is equal to the sample mean = 1490
b. Stdev of T is given by Stdev of population = 300
c. Stdev of M is Stdev of population / sqrt(n) = 300/sqrt(36) = 50
d. We divide 53000 by 36 to convert for a per person number: P(X<53000/36) = P(X<1472.22) = P(Z< (1472.22-1490)/sqrt(36)) = P(Z<-2.96) = .0015
e. P(1425<X<1575) = P( (1425-1472.2)/50 <Z< (1575-1472.2)/50)) = P(-.944<Z<2.056) = .8075
f. --

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