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

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