Answer :
Answer:
97.7% of of the boxes weigh more than 22.9 ounces.
15.9% of of the boxes weigh less than 23.7 ounces.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 24.5 ounces
Standard Deviation, σ = 0.8 ounce
We are given that the distribution of boxes weight is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(boxes weigh more than 22.9 ounces)
P(x > 22.9)
[tex]P( x > 22.9) = P( z > \displaystyle\frac{22.9 - 24.5}{0.8}) = P(z > -2)[/tex]
[tex]= 1 - P(z \leq -2)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 22.9) = 1 - 0.023 =0.977= 97.7\%[/tex]
97.7% of of the boxes weigh more than 22.9 ounces.
b) P(boxes weigh less than 23.7 ounces)
P(x < 23.7)
[tex]P( x < 23.7) = P( z < \displaystyle\frac{23.7 - 24.5}{0.8}) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 23.7) =0.159= 15.9\%[/tex]
15.9% of of the boxes weigh less than 23.7 ounces.