SOLUTION: Among a certain population of primates, the volume of the cranial cavity is normally distributed with a mean of 1000 cc and a standard deviation of 117 cc. (a) What percentage of

Question 1141826: Among a certain population of primates, the volume of the cranial cavity is normally distributed with a mean of 1000 cc and a standard deviation of 117 cc.
(a) What percentage of primates will have a volume of the cranial cavity smaller than 950
cc?
(b) What percentage of primates will have a volume of the cranial cavity between 1000 cc
and 1350 cc?
(c) What percentage of primates will have a volume of the cranial cavity larger than 1250
cc?
(d) We are selecting five members of this population at random. What is the probability that
all of the 5 selected primates will have a volume of the cranial cavity that is larger than
1150 cc?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd or (x bar-mean)sigma/sqrt(n) if a sample is used
a. z<(950-1000)/117 or <-0.43 and that probability is 0.3336
b. this is z between 0 and 350/117 or between 0 and 3 or 0.4986 probability
c. greater than 1250 cc is z>250/117 or 2.14 for a probability of 0.0162
d. here it is z>(150/117)*sqrt(5) or z>2.87 or probability of 0.0021
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