The weights of a certain animal species are approximately normally distributed w
ID: 2979598 • Letter: T
Question
The weights of a certain animal species are approximately normally distributed with a mean of 4.2 lb. and a standard deviation of 1.1 lb.
a) What is the probability that a randomly selected animal weighs between 3 lb. and 5 lb.?
b) What is the probability the mean weight from a random sample of 8 animals is between 3 lb. and 5 lb.?
c) What is the probability that a randomly selected animal weighs more than 6 lb.?
d) What is the probability that the mean weight from a random sample of 8 animals is more than 6 lb.?
Explanation / Answer
a>
the probability is P[((3-4.2)/1.1)<z<((5-4.2)/1.1))]=P(-1.09<z<.727)=.629
b>
for 8 animals, P[(sqrt(8)*(3-4.2)/1.1)<z<(sqrt(8)*(5-4.2)/1.1))]=P(-3.08<z<2.05)=.97
c>
P[((6-4.2)/1.1)>z]=1-P[((6-4.2)/1.1)<z]=.052
d>
P[(sqrt(8)*(6-4.2)/1.1)>z]=1-P[(sqrt(8)*(6-4.2)/1.1)<z]=.001
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