SOLUTION: The heights of 200 plants in a garden follow a normal distribution with a mean of 72.3 cm with a standard deviation of 8.9 cm. a. about how many plants whose heights are between

Question 1181573: The heights of 200 plants in a garden follow a normal distribution with a mean of 72.3 cm with a standard
deviation of 8.9 cm.
a. about how many plants whose heights are between 82 and 90 cm?
b. about how many plants whose heights are between 70 and 75 cm?
c. if 20% of the tallest plants are to be trimmed, then what is the starting height of the plants that the
gardener must choose to trim?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
a. z=9.7/8.9 and 17.7/8.9 or 1.09 and 1.99. That probability is 0.1146
b. z=-2.3/8.9 and 2.7/8.9 or -0.26 and 0.30 with probability of 0.2204
check with 2nd VARS2normalcddf(82,90,72.3,8.9) which is more accurate because the z-values above were rounded, But it is only to the fourth decimal place in the first and 0.0008 different in the second. Ask how accurate it should be.
c.80th percentile has a z of 0.8416. (can use 3invnorm(0.80,0,1) to get the z-value
so 0.846=(x-72.3)/8.9
7.49=x-72.3
x=79.8 cm
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