Can someone give me a heads up on how to even start this problem..
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.
It helps to make a sketch of the bell-curve to visualize the problem.
Mark off any position to the right of the mean as your z-score
let the area below that z-score be x
you know the area below the mean is .5
x - .5 = .3989
x = .3989
I don't know if you use tables or some other method to do your calculations, but if you have tables you will have to find .3989 or the closest given value to that in the body of the tables
to get z = appr 1.275
I use this very useful webpage to do this tedious work
http://davidmlane.com/hyperstat/z_table.html
click on the second option: "Value from an area"
enter .8989 in "Area"
leave mean and SD as 0 and 1
click on "between" to get 1.275
your other two questions are done in the same way.
I put the information in as you said and I got for the second answer 0.66 and the last one 0.47 and they were wrong. What did I do wrong, I followed your instructions...
To solve these problems, you need to use the standard normal distribution table, also known as the z-table. This table provides the area under the standard normal curve for different z-values.
The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. In this case, we are looking for the z-score that corresponds to a given area under the curve.
Here's how you can solve each part:
(a) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3989.
1. Locate the given area (0.3989) in the z-table.
2. The z-score corresponding to this area will be the value you are looking for.
(b) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.4875.
1. Locate the given area (0.4875) in the z-table.
2. The z-score corresponding to this area will be the value you are looking for.
(c) Find the standard score (z) such that the area above the mean and below z under the normal curve is 0.3628.
1. Locate the given area (0.3628) in the z-table.
2. The z-score corresponding to this area will be the value you are looking for.
Remember to use the z-table that gives the areas under the curve to the left of the z-score. If you need the area above the mean and below z, subtract the given area from 1.
Once you have the z-scores, you can round them to two decimal places as requested in the question.