Question

Every​ quarter, the Food and Drug Administration​ (FDA) produces a report called the Total Diet Study. The​ FDA's report covers a variety of food​ items, each of which is analyzed for potentially harmful chemical compounds. A Total Diet Study reported that no pesticides at all were found in ​% of the domestically produced food samples. Consider a sample of food items analyzed for the presence of pesticides. Complete parts a and b. a. Compute and for the random variable​ x, the number of food items found that showed no trace of pesticide. nothing ​(Type an integer or a​ decimal.)

Answer 1

a) Mean = 600

Standard deviation = 12.24

B)No it is not likely because our probability of no pesticide is 75% which means that more than half of food items are without any pesticide

Explanation:

Total number of food items = 800

We are given that no pesticides were found at all in 75% of domestically produced food samples.

So, Probability of success = p = 0.75

Probability of failure = q = 1-p = 1-0.75=0.25

Now we are supposed to find
`\mu` and
`\sigma` for random variable x

a) Mean = E(x)=
`n * p = 800 * 0.75=600`

Standard deviation =
`√(npq)=√(800 * 0.75 * 0.25)=12.24`

b)Is it likely that you would observe fewer than half of the food items without any traces of pesticides ? Why or why not ?

No it is not likely because our probability of no pesticide is 75% which means that more than half of food items are without any pesticide