Question

An advertisement for jelly beans claims "At least 100 beans in every box.". The machine used to fill the boxes has been found to fill boxes with a mean of 108 beans and a standard deviation of 3 beans. What is the probability that the advertising claim is true?Choose one answer. a. 0.996b. 0.998c. 0.500d. 0.994

Answer 1

`\begin{gathered} \mu=108 \\ \sigma=3 \end{gathered}`

So,

`\begin{gathered} P(X\ge100)=P(Z\ge(X-\mu)/(\sigma))=P(Z\ge(100-108)/(3)) \\ so: \\ P(Z\ge-(8)/(3)) \end{gathered}`

Using the z-table:

`P(Z\ge-(8)/(3))\approx0.9962`

Answer:

a. 0.996