Answer:
The parcel with weight less than 20.14 pounds are 99% of all parcels under the surcharge weight.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 12 pounds
Standard Deviation, σ = 3.5 pounds
We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.99
[tex]P( X < x) = P( z < \displaystyle\frac{x - 12}{3.5})=0.99[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 12}{3.5} = 2.326\\\\x = 20.141\approx 20.14[/tex]
Thus, parcel with weight less than 20.14 pounds are 99% of all parcels under the surcharge weight.
