# Math Help - Help! standard deviation

1. ## Help! standard deviation

Can anyone help me with the following questions? My daughter was up all night and I'm not with it today! THANKS!!!!

A normal distribution has a mean of 21.8 and a standard deviation of 1.4. What is the z score for a value of 18.3?

A normal distribution has a mean of 36 and a standard deviation of 3. What is the z score for a value of 42?

For a standard normal distribution, 95% of the data are within _____ standard deviations of the mean.

Using the region under the curve in a standard normal distribution, the cumulative area from the left for a z score of -1.645 is:?

2. A normal distribution has a mean of 21.8 and a standard deviation of 1.4. What is the z score for a value of 18.3?
$z=\frac{x-{\mu}}{\sigma}=\frac{18.3-21.8}{1.4}$

A normal distribution has a mean of 36 and a standard deviation of 3. What is the z score for a value of 42?
Same as above.

For a standard normal distribution, 95% of the data are within _____ standard deviations of the mean.
This is the 68-95-99.7 rule. 68% of the data is within 1 standard deviation of the mean. 95% is within 2 standard deviations of the mean and 99.7% of the data is within 3 standard deviations of the mean.

Using the region under the curve in a standard normal distribution, the cumulative area from the left for a z score of -1.645 is:?
Look up what corrsponds to -1.645 in the body of the z-table. It should be in your daughters stats book. Possibly in the front cover.