Question

Use the standard normal table to find the Z-score that corresponds to the cumulative area 0 2546. If the area is not in the table, use the entry closest bto the area. If thearea is halfway between two entries, use the z-score halfway between the corresponding Z-scores Z=_(Type an integer or decimal rounded to two decimal places as needed)

Answer 1

We have to find the z-score that correspond to an area under the curve of 0.2546.

This means to find the value of zc, so that:

$P(zWe have to look in the table the area 0.2546 and then relate it to a value of z.

We already know that z will be negative as the area for values larger than 0 are 0.5 or more.

In the table, the first column indicates the values of z. Then, the different columns add decimals to the value of z in each row, to have more precision.

We then can look for the area value of 0.2546 as:

We start looking in the column with decimal 0.00 to find the closest area.

As we are looking for an area of 0.2546, we stop at 0.2451, which corresponds to z = -0.6.

If we continue to -0.5, we would have a larger area, so we have to stop at the row for z = -0.6.

Then, we move to the right until we find the exact value or, more commonly, a range that includes the area we are looking for.

In this case, we find the exact area, and it correspond to the column ".06".

Then, we can express zc as:

[tex]z_c=-(0.6+0.06)=-0.66$

We can check with an app as:

We have confirmed we have the right value:

$P(z<-0.660)\approx0.2546$

Answer: z-score = -0.66