Question

In an Oreo factory, the mean mass of a cookie is given as40 grams with a standard deviation of 2 grams. Whatpercentage of the cookies are between 34 grams and 42grams?

Answer 1

The Solution:

Given:

`\begin{gathered} \bar{x}=mean=40g \\ \sigma=\text{ standard deviation}=2g \end{gathered}`

We are required to find the percentage that is between 34 grams and 42 grams.

By z-score statistic,

The lower limit is:

`Z_1=(x-\mu)/(\sigma)=(34-40)/(2)=(-6)/(2)=-3`

The upper limit is:

`Z_2=(x-\mu)/(\sigma)=(42-40)/(2)=(2)/(2)=1`

The probability is:

`P(Z_1Converting to percent, we multiply by 100:[tex]0.840*100=84\text{\%}`

Therefore, the correct answer is 84%