Here is how to do that conversion...
The heights of fully grown sugar maple trees are normally distributed, with a mean of 87.5 feet and a standard deviation of 6.25
feet. Random samples of size 12 are drawn from the population. Find the probability that the mean height of the tree is less than 86 feet.
1 answer:
Answer:
20.33%
Step-by-step explanation:
We have that the mean (m) is equal to 87.5, the standard deviation (sd) 6.25 and the sample size (n) = 12
They ask us for P (x <86)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (86 - 87.5) / (6.25 / (12 ^ 1/2))
z = -0.83
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <-0.83) = 0.2033
The probability is 20.33%
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Step-by-step explanation:
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Statements A, B, and C are true.
Step-by-step explanation:
Step 1:
A cone, a cylinder and a sphere all have radii of 3 inches. The cone and cylinder have heights of 2 inches.
The volume of the cone, Here r = 3 inches and h = 2 inches.
So the volume of the cone cubic inches.
The volume of the cylinder, Here r = 3 inches and h = 2 inches.
So the volume of the cylinder = cubic inches.
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Step 2:
Now we check to see which statements are true.
A. About 113 cubic inches of catnip will fit inside a sphere-shaped toy so it is true.
B. About 18.8 cubic inches of catnip will fit inside a cone-shaped toy so it true.
C. The sphere-shaped toy holds the most of the three so it is true.
D. No shape holds 169.6 cubic inches, so D is false.
E. The toys shaped like a cone and a cylinder do not hold the same amount of catnip in them. So it is false.
P.S. I couldn't see the options B, D, and E completely.