Question

A random variable X follows the uniform distribution with a lower limit of 720 and an upper limit of 920. 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 870?

Answer 1

Answer:

a. mean = 820; standard deviation = 57.74

b.0.75 or 75%

Step-by-step explanation:

Lower limit (L) = 720

Upper limit (U) =920

a.The mean of an uniform distribution is given by:

$\mu = \frac{L+U}{2}=\frac{720+920}{2}\\ \mu = 820$

The standard deviation of an uniform distribution is given by:

$\sigma = \frac{U-L}{\sqrt{12}} = \frac{920-720}{\sqrt{12}}\\\sigma=57.74$

b. The probaility that X is less 870 is:

$P(X$