Question

A set of exam scores is normally distributed with a mean = 80
and standard deviation = 10.

Use the **Empirical Rule** to complete the following
sentences.

68% of the scores are between _____ and ______.

95% of the scores are between ______ and _______.

99.7% of the scores are between _______ and ________.

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Answer #1

Solution :

Using Empirical rule,

P( - 1< X < + 1) = 68%

P(80 - 1 * 10 < X < 80 + 1 *10) = 68%

P(70 < X < 90) = 68%

68% of the scores are between 70 and 90

P( - 2< X < + 2) = 95%

P(80 - 2 * 10 < X < 80 + 2 * 10) = 95%

P(60 < X < 100) = 95%

95% of the scores are between 60 and 100

P( - 3< X < + 3) = 99.7%

P(80 - 3 * 10 < X < 80 + 3 * 10) = 99.7%

P(50 < X < 110) = 99.7%

99.7% of the scores are between 50 and 110

Assume that a set of test scores is normally distributed with a
mean of 80 and a standard deviation of 25. Use the 68-95-99.7 rule
to find the following quantities.
c. The percentage of scores between 30 and 105 is %.?
(Round to one decimal place as needed.)

Assume that a set of test scores is normally distributed with a
mean of 80 and a standard deviation of 20. Use the 68-95-99.7 rule
to find the following quantities.
The percentage of scores less than 80 is __%
The percentage of scores greater than 100 is _%
The percentage of scores between 40 and 100 is _%
Round to the nearest one decimal

Assume that a set of test scores is normally distributed with a
mean of 100 and a standard deviation of 10. Use the 68-95-99.7
rule to find the following quantities.
a. The percentage of scores less than 100 is __%
b. The percentage of scores greater than 110 is __%
c. The percentage of scores between 80 and 110 is __%
(Round to one decimal place as needed)

Suppose a normally distributed set of data has a mean of 193 and
a standard deviation of 13. Use the 68-95-99.7 Rule to determine
the percent of scores in the data set expected to be below a score
of 219. Give your answer as a percent and includeas many decimal
places as the 68-95-99.7 rule dictates. (For example, enter 99.7
instead of 0.997.)

A set of 1200 exam scores is normally distributed with a mean =
82 and standard deviation = 6.
Use the Empirical Rule to complete the statements
below.
How many students scored higher than 82?
How many students scored between 76 and 88?
How many students scored between 70 and 94?
How many students scored between 82 and 88?
How many students scored higher than 76?

Assume that a set of test scores is normally distributed with a
mean of 100 and a standard deviation of 10 . Use the 68-95-99.7
rule to find the following quantities. a. The percentage of scores
less than 110 is %. (Round to one decimal place as needed.) b.
The percentage of scores greater than 110 is nothing %. (Round to
one decimal place as needed.)

assume that a set of test scores is normally
distributed with the mean of 110 and a standard deviation of 15.
use the 86-95-99.7 rule

Assume that a set of test scores is normally distributed with a
mean of 100 and a standard deviation of 20. Use the 68-95-99.7
rule to find the following quantities. a. The percentage of scores
less than 100 is . (Round to one decimal place as needed.) b. The
percentage of scores greater than 120 . (Round to one decimal
place as needed.) c. The percentage of scores between 60 and 120
is nothing%. (Round to one decimal place as...

Suppose the scores of students on an exam are Normally
distributed with a mean of 303 and a standard deviation of 39. Then
approximately 99.7% of the exam scores lie between the numbers and
such that the mean is halfway between these two integers. (You are
not to use Rcmdr for this question.)

scores on the GRE are normally distorted with a mean of 570 and
a standard deviation of 92. use the 68-95-99.7 rule to find the
percentage of people taking the test who score between 294 and
846

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