Question

Suppose you sample one value from a uniform distribution with a = 0 and b= 50. a. What is the probability that the value will be between 35 and 45? b. What is the probability that the value will be between 6 and 23? c. What is the mean? d. What is the standard deviation? 1. a. The probability that the value will be between 35 and 45 is (Type an integer or a decimal.)

Answer 1

a)
Here, the given values of lower limit, a = 0 and upper limit, b = 50

For Uniform Distribution,
P(x1 <= X <= x2) = (x2 - x1)/(b - a)
P(35 <= X <= 45) = (45 - 35)/(50 - 0)
P(35 <= X <= 45) = 0.2

b)

Here, the given values of lower limit, a = 0 and upper limit, b = 50

For Uniform Distribution,
P(x1 <= X <= x2) = (x2 - x1)/(b - a)
P(6 <= X <= 23) = (23 - 6)/(50 - 0)
P(6 <= X <= 23) = 0.34

c)

Mean = (a + b)/2
Mean = (0 + 50)/2 = 25

d)

Standard Deviation = sqrt((b - a)^2/12)
Standard Deviation = sqrt((50 - 0)^2/12 = 14.4338