8p + 3q - when p=1/3 and q=7

The mean IQ score of students in a particular calculus class is 110, with a standard deviation of 5. Use the Empirical Rule to f

Anika [276]

Answer:

2.5%

Step-by-step explanation:

If the data set has a bell-shaped distribution, then you can use 68-95-99.7, or Empirical, rule. With bell-shaped distributions, 68% of results lie within 1 standard deviation of the mean, 95% of results lie within 2 standard deviations, and 99.7% lie within 3 standard deviations.

Your mean is 110, and you have a standard deviation of 5. This means that 68% of all students fall between IQ scores of 105 (110 - 5) and 115 (110 + 5), one standard deviation from the mean. To get 95% of the students, you need to go one more standard deviation out, so then you have 100 (105 - 5) and 120 (115 + 5), two standard deviations from the mean. 99.7% of the students fall between 95 (100 - 5) and 125 (120 + 5). What you want is to find the percentage of students with an IQ above 120.

The way I'd handle this is starting with what I know is absolutely, without a doubt, below 120. If you drew a quick bell curve to represent this data, everything to the left of the mean, 110, could be counted out right away (I usually color in half of the bell curve because I like the visual representation). Just like that, 50% of your data is gone. From there, I know 120 is right at 2 standard deviations away, so I color in all the way up to the 95% mark, but remember that when we took away 50%, you don't want to count all the standard deviations on the left side of the bell curve twice. So instead, take the 95% and cut it in half, which is 47.5%. Alternatively, you can start at 50% and count up 1 standard deviation (34%), and up one more (13.5%) and get the same result, 47.5%. So now you know 50 + 47.5 = 97.5% of results are LOWER than 120. To figure out what's higher than 120, all you have to do is see that

100% - 50% - 47.5% = 2.5%

And then you can see that 2.5% of students have an IQ over 120.

5 0

3 years ago

Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Zielflug [23.3K]

C: 1 × 4 × 4

D: 2 × 2 × 4

3 0

3 years ago

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 ce

julsineya [31]

Answer:

The proportion of students whose height are lower than Darnell's height is 71.57%

Step-by-step explanation:

The complete question is:

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnel is a middle school student with a height of 161.4cm.

What proportion of proportion of students height are lower than Darnell's height.

Answer:

We first calculate the z-score corresponding to Darnell's height using:

$Z=\frac{X-\mu}{\sigma}$