Question

Find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28. Round your answer to four decimal places, if necessary.

Answer 1

Answer:

The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

Step-by-step explanation:

We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.

The standard normal table represents the area under the curve.

$P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)$          .....(1)

According to the standard normal table, we get

$P(z<-2.94)=0.0016$

$P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887$

Substitute these values in equation (1).

$P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903$

Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

Answer 2

The area under the standard normal curve to the left of z  = −2.94 and to the right of z = −2.28 is 0.9903 square units.

What is normal a distribution?

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be

The standard normal table represents the area under the curve.

$\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)$ ...1

According to the standard normal table, we have

$\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887$

Substitute these values in equation 1, we have

$\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903$

More about the normal distribution link is given below.

https://brainly.com/question/12421652