Scores on a test are normally distributed with a mean of 70 and a standard deviation of 11.5. find p81, which separates the bottom 81% from the top 19%.

The score p81 that separates the bottom 81% from the top 19% is 80.12

Step by step:

First, calculate the "z" value. Z is a normally distributed random variable with 0 mean and standard deviation 1. The score value corresponding to the desired percentile p81 can be determined from a z value as follows:

We use a z-table (check online) to find the z value for the 81-st percentile. I found and so we use that value to calculate the score for the percentile:

The score p81 that separates the bottom 81% from the top 19% is 80.12

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1