Question

The weight distribution of parcels sent in a certain manner is normal with meanvalue 12 pounds and standard deviation 3.5 pounds. The parcel service wishes to establish aweight valuecbeyond which there will be a surcharge. What value ofcis such that 99% ofall parcels are under the surcharge weight?

Answer 1

The parcel with weight less than 20.14 pounds are 99% of all parcels under the surcharge weight.

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:

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

We have to find the value of x such that the probability is 0.99

`P( X < x) = P( z < \displaystyle(x - 12)/(3.5))=0.99`

Calculation the value from standard normal z table, we have,

`\displaystyle(x - 12)/(3.5) = 2.326\\\\x = 20.141\approx 20.14`

Thus, parcel with weight less than 20.14 pounds are 99% of all parcels under the surcharge weight.