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 25 and 40? b. What is the probability that the value will be between 3 and 22? c. What is the mean? d. What is the standard deviation? a. The probability that the value will be between 25 and 40 is (Type an integer or a decimal.) b. The probability that the value will be between 3 and 22 is (Type an integer or a decimal.) c. The mean of the given uniform distribution is u (Type an integer or a decimal.) d. The standard deviation of the given uniform distribution is o (Round to four decimal places as needed.)

Answer 1

Solution :

Given that,

a = 0

b = 50

a ) P (25 < X < 40 )

= (40 - 25) / (50 - 0)

= 15 / 50

= 0.3

Probability = 0.3

b ) P (3< X < 22 )

= (22 - 3) / (50 - 0)

= 19 / 50

= 0.38

Probability = 0.38

c ) mean  $\mu$ = (a + b) / 2

= ( 0 + 50 ) / 2

= 50 / 2

= 25

mean  $\mu$ = 25

standard deviation = $\sigma$ =  $\sqrt$ (b - a)² / 12

=  $\sqrt$(50 - 0 )² / 12

= $\sqrt$ 2500 /12

= $\sqrt$ 208.33

= 14.4336

standard deviation = $\sigma$ = 14.4336