Consider the following. (Give your answers correct to four decimal places.)
(a) Determine the level of confidence given the confidence coefficient z(á/2) for z(á/2) = 1.65.
Incorrect: Your answer is incorrect. .
(b) Determine the level of confidence given the confidence coefficient z(á/2) for z(á/2) = 1.93.
Incorrect: Your answer is incorrect. .
(c) Determine the level of confidence given the confidence coefficient z(á/2) for z(á/2) = 2.17.
(d) Determine the level of confidence given the confidence coefficient z(á/2) for z(á/2) = 2.41.
To determine the level of confidence given the confidence coefficient z(á/2), we need to find the area under the standard normal distribution curve to the right of z(á/2). Here's how you can do it:
(a) Given z(á/2) = 1.65, we want to find the level of confidence.
First, we need to look up the area to the right of 1.65 in the standardized normal distribution table. The area in the table corresponds to the area from negative infinity up to z(á/2).
Looking up the value for 1.65 in the standardized normal distribution table, we find that the area to the right of 1.65 is approximately 0.0495.
Since the total area under the curve is 1, the level of confidence is 1 - 0.0495 = 0.9505, or 95.05% confidence.
So the level of confidence for z(á/2) = 1.65 is 95.05%.
(b) Given z(á/2) = 1.93, we want to find the level of confidence.
Using the same process as before, we look up the area to the right of 1.93 in the standardized normal distribution table. The area to the right of 1.93 is approximately 0.0274.
The level of confidence is then 1 - 0.0274 = 0.9726, or 97.26% confidence.
So the level of confidence for z(á/2) = 1.93 is 97.26%.
(c) Given z(á/2) = 2.17, we want to find the level of confidence.
Again, we look up the area to the right of 2.17 in the standardized normal distribution table. The area to the right of 2.17 is approximately 0.0152.
The level of confidence is 1 - 0.0152 = 0.9848, or 98.48% confidence.
So the level of confidence for z(á/2) = 2.17 is 98.48%.
(d) Given z(á/2) = 2.41, we want to find the level of confidence.
Looking up the area to the right of 2.41 in the standardized normal distribution table, we find that the area is approximately 0.0071.
The level of confidence is 1 - 0.0071 = 0.9929, or 99.29% confidence.
So the level of confidence for z(á/2) = 2.41 is 99.29%.