Find the mean and standard deviation of the specified probab

Find the mean and standard deviation of the specified probability density function.

f(x) = 4 for [2.25, 2.50]

a. = 2.500, = .069
    b. = 2.500, = .070
    c. = 2.375, = .072
    d. = 2.375, = .144

Solution

here X folows uniform distribution

mean = (2.25 + 2.50 )/2 = 2.375

variance = 1/12 * (2.50 -2.25)^2 = 1/192

standard deviation = sqrt(variance) = 0.072

hence correct choice is c)