Answer:
58.9% produced produced peppers weighing between 13 and 16 pounds.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(peppers weighing between 13 and 16 pounds)
[tex]P(13 \leq x \leq 16) = P(\displaystyle\frac{13 - 15}{1.75} \leq z \leq \displaystyle\frac{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\%[/tex]
[tex]P(13 \leq x \leq 16) = 58.9\%[/tex]
58.9% produced produced peppers weighing between 13 and 16 pounds.
