Scores on the gre (graduate record examination) are normally distributed with a mean of 600 and a standard deviation of 120. use the 68 dash 95 dash 99.7 rule to find the percentage of people taking the test who score between 240 and 960.

99.7%

Step-by-step explanation:

The 68-95-99.7 rule refers to what percentage of data is contained within ranges a certain distance from the mean.

68% of the data lies within one standard deviation of the mean

95% lies within two standard deviations, and

99.7% lies within three standard deviations.

Our mean here is 600, and our standard deviation is 120, so those ranges would be:

480-720 for 1 standard deviation

360-840 for 2 standard deviations, and

240-960 for 3.

Our given range is 240 to 960, three standard deviations from the mean, so the 68-95-99.7 rule tells us that this range contains 99.7% of the people.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23