Problem

Use the standard normal table to find the $z$-score that corresponds to the cumulative area 0.9808 . If the area is not in the table, use the entry closest to the area. If the area is halfiray between two entries, use the $z$-score halfway between the corresponding $z$-scores. Click to view page 1 of the standard normal table. Click to view page 2 of the standard normal table. \[ z= \] (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Step 1 :We are given a cumulative area of 0.9808 under the standard normal distribution curve and we are asked to find the corresponding z-score.

Step 2 :The z-score is the number of standard deviations a given data point is from the mean.

Step 3 :We can use the inverse of the cumulative distribution function to find the z-score. The inverse of the cumulative distribution function gives the z-score that corresponds to a given cumulative area.

Step 4 :Using the inverse of the cumulative distribution function, we find that the z-score that corresponds to the cumulative area 0.9808 is approximately 2.07.

Step 5 :This means that a cumulative area of 0.9808 is 2.07 standard deviations above the mean in a standard normal distribution.

Step 6 :Final Answer: The z-score that corresponds to the cumulative area 0.9808 is approximately \(\boxed{2.07}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8874/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download