The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 85 and standard deviation 12. What intelligence score will place a child in the 95th percentile?
have this intelligence test that we're told is approximately normal With a mean of 85 and a standard deviation of 12. And so that distribution looks like this Centered at 85. And again, this is 12 units away. So that would be up at 97. And you want to find where the 95th%ile is. So the 95th%ile Is going to have 95% of the area this way. So this is an area of .95. And so you should look up in your table 0.95 and you're going to find it's halfway between A z value of 1.64 and 1.65. So typically we use 1.645 because it's five point 9495.9505. And so we go halfway in between. And so depending on how you do it, you can just use your standard Z score and plug in the values and say this disease score is here, excuse me, your main is here and your standard deviation goes here and then sobbing for X. You'll end up getting the 85 Plus 1.645 times 12. And this value comes out to be 104.74. You raise that To be a seven there. Truth. So there's the value. Now you probably can't get a decimal score. So approximately 105 Would be the 95th%ile and maybe your professor might have you round down. I'm not sure. So anyway, that's your calculation