A random variable X follows the uniform distribution with a

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 of this 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? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solution

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 of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)

Expectation = (a+b)/2 (670+750)/2 = 710

Variance = (b-a)²/12 = 533.3333

Standard deviation = 23.09

b. What is the probability that X is less than 730? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

P( x <730) = 0.75