For the following question, first identify what type of scenario is involved (Bi

Question

For the following question, first identify what type of scenario is involved (Binomial, Normal Population Distribution, Normal Sampling Distribution, Hypothesis Test). Then go back and solve. For each scenario involving a normal distribution, draw a picture to represent the normal distribution. Then shade for the scenarios given.

3.) The average age of trees in a large local park is 60 years with a standard deviation of 2.2 years. A simple random sample of 400 trees is selected, and the sample mean age x of these trees is computed.

a.) Find the probability that the average age x of the 400 trees is more than 60.1 years.

b.) Find the probability that the average age x of the 400 trees is between 59.8 and 60.3 years

Explanation / Answer

The sample mean is same as population mean=60 and the sample standard deviation is sigma/root over n

=2.2/root over 400

=0.11

a)For X bar=60.1, z=(x bar-mu)/0.11

=0.90

P(X bar>60.1)=1-P(X bar<60.1)

=1-P(z<0.90)

=1-0.8159

=0.1841

b)For X=59.8, z=(59.8-60)/0.11=-1.81

For X=60.3, z=(60.3-60)/0.11=2.72

Thus, P(59.8<X<60.3)=P(X<60.3)-P(X<59.8)

=P(z<2.72)-P(z<-1.81)

=0.9967-0.0351

=0.9616

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