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

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:

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8