Question

find the area under the standard normal curve. use excel. round the answers to at least four decimal places.
part 1 of 4
(a) find the area under the standard normal curve that lies between z = -2.48 and z = -1.33.
the area between z = -2.48 and z = -1.33 is 0.0852.
part 2 of 4
(b) find the area under the standard normal curve that lies outside the interval between z = -2.45 and z = -0.34.
the area outside the interval between z = -2.45 and z = -0.34 is 0.6402.
part 3 of 4
(c) find the area under the standard normal curve to the left of z = -2.16.
the area to the left of z = -2.16 is \boxed{}.

Explanation:

Step1: Recall Excel function for normal distribution

To find the area to the left of a z - score \(z\) in the standard normal distribution, we can use the Excel function NORM.S.DIST(z, TRUE), where the second argument TRUE indicates that we want the cumulative distribution function (which gives the area to the left of the z - score).

Step2: Apply the function for \(z = - 2.16\)

We use the formula NORM.S.DIST(-2.16, TRUE) in Excel. When we calculate this, we get the area to the left of \(z=-2.16\).

Calculating NORM.S.DIST(-2.16, TRUE) in Excel (or using a standard normal table approximation), we know that the standard normal distribution is symmetric, and the cumulative probability for \(z=-2.16\) can be found. The value of NORM.S.DIST(-2.16, TRUE) is approximately \(0.0154\).

Answer:

\(0.0154\)