Question

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X= percent of fat calories.(a) Find the z-score corresponding to 30 percent of fat calories, rounded to 3 decimal places.

Answer 1

The formula for Z-score is given as,

`Z=(X-\mu)/(\sigma)`

Given that

Therefore,

`\begin{gathered} Z=(30-36)/(10)=(-6)/(10)=-0.6 \\ \therefore Z=-0.6 \end{gathered}`

Hence,

`\begin{gathered} Z=-0.6\approx-0.600(3\text{ decimal places)} \\ \therefore Z=-0.600 \end{gathered}`