We have no ideal on how to start this problem, we have look for it on the charts, did not see. Please help
Consider the following. (Give your answers correct to two decimal places.)
(a) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989.
(b) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875.
(c) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628.
To solve this problem, we can use a standard normal distribution table or a calculator with a normal distribution feature.
(a) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989:
Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the area of 0.3989.
Looking up the area 0.3989 in the table or using a calculator, we find that the z-score is approximately 0.25.
Therefore, the standard score (z) that corresponds to an area of 0.3989 is approximately 0.25.
(b) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875:
In a similar way, we can find the z-score corresponding to the area of 0.4875.
Looking up the area 0.4875 in the table or using a calculator, we find that the z-score is approximately 0.00 (or very close to the mean).
Therefore, the standard score (z) that corresponds to an area of 0.4875 is approximately 0.00.
(c) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628:
Again, we can find the z-score corresponding to the area of 0.3628.
Looking up the area 0.3628 in the table or using a calculator, we find that the z-score is approximately -0.36.
Therefore, the standard score (z) that corresponds to an area of 0.3628 is approximately -0.36.
To solve this problem, you can use a standard normal distribution table or a calculator with a built-in standard normal distribution function. Here's how you can find the answers:
(a) To find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989, you need to look for the corresponding z-value in the standard normal distribution table. The area between the mean and any z-value on the standard normal distribution curve represents the cumulative probability up to that value.
By searching for the closest area value of 0.3989 in the standard normal distribution table, you can find the corresponding z-value. Typically, the table provides the area to the left of the z-value, so you may need to subtract 0.3989 from 1 to get the corresponding area to the right.
(b) Similarly, to find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875, you can use the same method as in (a) by searching for the closest area value of 0.4875 in the standard normal distribution table.
(c) Once again, to find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628, you can use the same method as in (a) and (b) by searching for the closest area value of 0.3628 in the standard normal distribution table.
Remember to round your answers to two decimal places as specified in the question.
Note: If you have a calculator with a built-in standard normal distribution function, you can directly input the probability value to find the corresponding z-value without using the standard normal distribution table.