Does anyone know how to solve these two problems.

Solve the problem. Find the critical value za/2 that corresponds to a degree of condfidence of 98%.

Express the confidence interval in the form of ^p _+E.

0.033<p>0.493

Confidence interval using proportions:

CI98 = p + or - (2.33)(sqrt of pq/n)
...where + or - 2.33 represents 98% confidence using a z-table.
(q = 1 - p ...and... n = sample size)

I hope this helps.

To answer the first problem, we need to find the critical value zα/2 that corresponds to a degree of confidence of 98%.

Step 1: Identify the level of confidence.
In this problem, the level of confidence is 98%.

Step 2: Divide the level of confidence by 100.
To use the z-table, we need to express the level of confidence as a decimal. So, divide 98 by 100 to get 0.98.

Step 3: Subtract the decimal value from 1 and divide by 2.
Since the table only provides values for the area below the standard normal curve, we need to find the value for α/2. Subtracting the level of confidence from 1 and dividing by 2 will give us α/2.
(1 - 0.98) / 2 = 0.01 / 2 = 0.005

Step 4: Look up the value from the z-table.
Using the z-table, find the value closest to 0.005 or 0.0050 in the middle column. The corresponding value from the left column will be the critical value za/2.

The critical value za/2 that corresponds to a degree of confidence of 98% is approximately 2.33.

For the second problem, we need to express the confidence interval in the form of ^p ± E.

The interval notation ^p ± E represents the sample proportion (^p) plus or minus the margin of error (E).

Given that 0.033 < p < 0.493, we can calculate the sample proportion (^p) by taking the average of the lower and upper bounds:

^p = (0.033 + 0.493) / 2 = 0.263

Next, find the margin of error (E) by subtracting the lower bound from the sample proportion:

E = ^p - p(lower bound) = 0.263 - 0.033 = 0.23

Therefore, the confidence interval in the form of ^p ± E is:
0.263 ± 0.23