Question

A new experimental strain of pepper plants was being studied to estimate how much fruit one plant would produce in a typical growing season. The mean weight of peppers produced per plant was 15.0 pounds, with a standard deviation of 1.75 pounds. The weights were normally distributed. There were 200 plants in the experiment. How many plants would you estimate produced peppers weighing between 13 and 16 pounds

Answer 1

58.9% produced produced peppers weighing between 13 and 16 pounds.

Explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1.75

We are given that the distribution of weight of peppers is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(peppers weighing between 13 and 16 pounds)

`P(13 \leq x \leq 16) = P(\displaystyle(13 - 15)/(1.75) \leq z \leq \displaystyle(16-15)/(1.75)) = P(-1.142\leq z \leq 0.571)\\\\= P(z \leq 0.571) - P(z < -1.142)\\= 0.716 - 0.127 = 0.589 = 58.9\%`

`P(13 \leq x \leq 16) = 58.9\%`

58.9% produced produced peppers weighing between 13 and 16 pounds.