Question

1 point
The weights of laboratory cockroaches follow a Normal distribution with
mean 80 grams and standard deviation 2 grams. Use the figure from above.
About what percent of the cockroaches have weights less than 78 grams?
16%
none of these
32%
34%
O 2.5%

Answer 1

Answer:

16% of the cockroaches have weights less than 78 grams.

Option A is correct.

Step-by-step explanation:

Mean = 80 g

Standard Deviation = 2

We need to find percent of the cockroaches have weights less than 78 grams so, x=78

First we will find z using formula:

$z=\frac{x-\mu}{\sigma}$

Putting values of x, mean and Standard Deviation to find z

$z=\frac{x-\mu}{\sigma}\\z=\frac{78-80}{2}\\z=-1$

We need to find P(z<-1)

Looking in the normal distribution table

$P(z<-1)=0.15866\\P(z<-1)\approx 0.16\\Converting \ into \ percentage\\P(z<-1)=16\%$

So, 16% of the cockroaches have weights less than 78 grams.

Option A is correct.