Question

(1 point) Find the z−scorez−score from a standard normal distribution that satisfies each of the following statements. Round to two decimal places. (a) Determine the value of zz for which 2.09 percent of the area is below. z=z= (b) Find the closest point zz with 42.18 percent of the area to the right. z=z=

Answer 1

a) For this case we want a quantile that accumulate 2.09% of the data below or 0.0209 of the area below and we can use the following excel code:

"=NORM.INV(0.0209,0,1)"

`z = -2.036`

b) For this case we want a quantile that accumulate 42.18% of the data below or 0.4218 of the area below and we can use the following excel code:

"=NORM.INV(0.4218,0,1)"

`z = -0.197`

Explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Part a

For this case we want a quantile that accumulate 2.09% of the data below or 0.0209 of the area below and we can use the following excel code:

"=NORM.INV(0.0209,0,1)"

`z = -2.036`

Part b

For this case we want a quantile that accumulate 42.18% of the data below or 0.4218 of the area below and we can use the following excel code:

"=NORM.INV(0.4218,0,1)"

`z = -0.197`