## A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750. a. Calculate the mean and the stan

Question

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750. a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.) b. What is the probability that X is less than 730

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2 months 2021-10-13T23:30:06+00:00 1 Answer 0 views 0

## Answers ( )

a)

The variance is given by:

And the deviation is just the square root of the variance and we got:

b)

And for this case we can use the cumulative distribution given by:

And replacing we got:

Step-by-step explanation:

For this case we assume that X is our random variable and we know that the distribution for X is given by:

Part a

For this case the expected value is given by:

The variance is given by:

And the deviation is just the square root of the variance and we got:

Part b

For this case we want to find this probability:

And for this case we can use the cumulative distribution given by:

And replacing we got: