Question

A) A distribution of values is normal with a mean of 43.2 and a standard deviation of 61.9. Find P94, which is the score separating the bottom 94% from the top 6%. P94 = Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. B) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1536 and a standard deviation of 304. The local college includes a minimum score of 1840 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? P(X < 1840) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

          A) A distribution of values is normal with a mean of 43.2 and a
standard deviation of 61.9. Find P94, which is the score separating
the bottom 94% from the top 6%. P94 = Enter your answer as a number
accurate to 1 decimal place. Answers obtained using exact z-scores
or z-scores rounded to 3 decimal places are accepted.
B) The combined SAT scores for the students at a local high
school are normally distributed with a mean of 1536 and a standard
deviation of 304. The local college includes a minimum score of
1840 in its admission requirements.
What percentage of students from this school earn scores that fail
to satisfy the admission requirement?
P(X < 1840) = %
Enter your answer as a percent accurate to 1 decimal place (do not
enter the "%" sign). Answers obtained using exact z-scores
or z-scores rounded to 3 decimal places are accepted.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jason Horton

04/18/2022

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2 and a standard deviation of 61.9. Show more…

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A) A distribution of values is normal with a mean of 43.2 and a standard deviation of 61.9. Find P94, which is the score separating the bottom 94% from the top 6%. P94 = Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. B) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1536 and a standard deviation of 304. The local college includes a minimum score of 1840 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? P(X < 1840) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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0:00 All right, you have two questions here.

00:01 The first one is it says a distribution of values is normal with a mean of 43 .2 and a standard deviation of 61 .9.

00:10 You're trying to find what they're calling p94, which is the value that separates the lower 94 % of this distribution.

00:23 The first step in that process is going to be to find a z value for that number, a z score for that number.

00:30 And we're going to have to use the percentage that we're given to find it.

00:34 So i'm going to go to a z table, and i'm going to look up 0 .94 to try to find that z value.

00:48 Okay, so looking for 0 .94, the closest thing we can find, looks to be right here.

00:59 And it looks to me like 0 .94 would be exactly in the middle of those two highlighted values.

01:08 So the z score that i'm looking at would be a 1 .55, right in the middle, 5.

01:15 So i'm going to say 1 .555 is the z score that is associated with 94 % of the data being below it.

01:27 Okay, so now we'll bring that back, and now we know what z is, 1 .555.

01:34 Now we'll have to use a z score formula, which is where we take our x value, which is what we're looking for.

01:41 Minus the mean divided by the standard deviation.

01:46 So we know what z is.

01:47 It's 1 .555.

01:50 X is unknown.

01:52 Mean is 43 .2.

01:55 And standard deviation is 61 .9.

01:58 And now it just doesn't matter of solving that equation for x.

02:02 So i'm going to start by multiplying by 61 .9.

02:13 I get 93, or i'm sorry, 96 .2545.

02:24 Equals x minus 43 .2 and then add 43 .2 to both sides.

02:37 And we find this value that we're looking for is equal to 139 .4545.

02:51 Now, it says enter your answer is a decimal accurate to one decimal place...

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