$$ X $$ is a normally distributed random variable with mean 36 and standard deviation 20 . What is the probability that $$ X $$ is between 16 and 96 ? Use the $$ 0.68-0.95-0.997 $$ rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

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To find the probability that $$ X $$ is between 16 and 96, we can use the 68-95-99.7 rule for a normal distribution.

Given:
- Mean ($$ \mu $$) = 36
- Standard Deviation ($$ \sigma $$) = 20

The 68-95-99.7 rule states that:
- About 68% of the data falls within 1 standard deviation of the mean.
- About 95% of the data falls within 2 standard deviations of the mean.
- About 99.7% of the data falls within 3 standard deviations of the mean.

Since we are interested in the probability that $$ X $$ is between 16 and 96, we need to find the range within 2 standard deviations of the mean.

1 standard deviation = 20
2 standard deviations = 2 * 20 = 40

The range within 2 standard deviations of the mean is from 36 - 40 to 36 + 40, which is from 16 to 96.

Therefore, the probability that $$ X $$ is between 16 and 96 is approximately 95% or 0.95.
The probability that $$ X $$ is between 16 and 96 is 0.95.

is a normally distributed random variable with mean 36 and standard deviation 20 .
What is the probability that is between 16 and 96 ?
Use the rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.

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is a normally distributed random variable with mean 36 and standard deviation 20 . What is the probability that is between 16 and 96 ? Use the rule and write your answer as a decimal. Round to the nearest thousandth if necessary.