The Interior Department reports annually on the status of the country’s national

Question

The Interior Department reports annually on the status of the country’s national forests. In a recent survey done in John Muir Woods in California, the Department used a normal curve to describe the age distribution of trees in the forest. The distribution has a mean of 145 years and a standard deviation of 32 years.

1.What percentage of the trees is less than 57 years old?  (Round answer to 2 decimal places, e.g. 1.50%.)

2.What percentage of the trees is between 170 and 220 years old?  (Round answer to 2 decimal places, e.g. 1.50%.)

3.Logging is permitted in the forest, but the government bans the cutting of any trees that are more than 75 years old.

What percentage of the trees is off limits? (Round answer to 2 decimal places, e.g. 1.50%.)

Explanation / Answer

Mean is 145 and s is 32. z is (x-mean)/s

a) P(x<57)=P(z<(57-145)/32)=P(z<-2.75) or 1-P(z<2.75). from normal distribution table we get 1-0.9970 =0.003

b) P(170<x<220) =P((170-145)/32<z<(220-145)/32)=P(0.78<z<2.34) or P(z<2.34)-P(z<0.78) from normal table we get 0.9904-0.7823 =0.2081

c) P(x>75)=P(z>(75-145)/32)=P(z>-2.19) or P(z<2.19) from normal table is 0.9857

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