Question

Suppose that the diameters of oak trees are normally distributed with a mean of 4 feet and a standard deviation of 0.375 feet. Step 1 of 5: What is the probability of walking down the street and finding an oak tree with a diameter of more than 4.875 feet? [Remember to round probabilities to 4 decimal places] Step 2 of 5: What is the probability that the tree you find is between 4.2 and 5 feet in diameter? Step 3 of 5: Interpret your probability from the previous step. Step 4 of 5: If we wanted to look at the top 26% of trees, what would their minimum diameter be? [Round to 2 decimals] Step 5 of 5: If we know that all the trees in our neighborhood are in the bottom 12% of tree diameters, what is the largest one we could expect to find?

Answer 1

Step 1 of 5:

for normal distribution z score =(X-μ)/σx
here mean=       μ=	4
std deviation   =σ=	0.3750

probability =

P(X>4.875)

=

P(Z>2.33)=

1-P(Z<2.33)=

1-0.9901=

0.0099

Step 2 of 5: :

probability =

P(4.2<X<5)

=

P(0.53<Z<2.67)=

0.9962-0.7019=

0.2943

Step 4 of 5:

for 74th percentile critical value of z=		0.64
therefore corresponding value=mean+z*std deviation=			4.24

Step 5 of 5:

for 12th percentile critical value of z=		-1.17
therefore corresponding value=mean+z*std deviation=			3.56