Question

A random variable follows the continuous uniform distribution between 45 and 135. ​a) Calculate the probability below for the distribution. ​P(75less than or equalsxless than or equals125​) ​b) What are the mean and standard deviation of this​ distribution? ​a) ​P(75less than or equalsxless than or equals125​)equals nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

a = 45

b = 135

a ) P(75< x < 125 )

= (135- 125) / (135 - 45)

= 10 /90

=0.1111

Probability = 0.111

b ) mean = (a + b) / 2

= (45 +135 )/ 2

= 180 /2

= 90

Mean = 90

standard deviation =  (b - a)²/12  

=(135 - 45) / 12

=90 /12

=7.5

= 2.739

standard deviation = 2.739