Question

A random variable follows the continuous uniform distribution between 25 and 45.

​a) Calculate the probabilities below for the distribution. ​

1) ​P(xless than or equals40​)

​2) ​P(xequals41​)

​b) What are the mean and standard deviation of this​ distribution?

​a)​

1) ​P(xless than or equals40​)equals nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)

​2) ​P(xequals41​)equals nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)

​b) The mean of this distribution is nothing. ​(Type an integer or decimal rounded to two decimal places as​ needed.)

The standard deviation of this distribution is nothing. ​(Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

Solution:

We are given that random variable follows uniform distribution.

We are given a=25, b=45

Part a.1

We have to find P(X≤40)

P(X≤x) = (x – a)/(b – a)

P(X≤40) = (40 – 25)/(45 – 25) = 15/20 = 0.75

Required probability = 0.750

Part a.2

Here, we have to find P(X=41)

P(X=41) = 0.000

Required probability = 0.000

(Exact probability for any continuous distribution is equal to zero.)

Part b

Mean = (a + b)/2 = (25 + 45)/2 = 70/2 = 35

Mean = 35.00

Variance = (b – a)^2/12 = (45 – 25)^2/12 = 400/12 = 33.33333

Variance = 33.33

Standard deviation = sqrt((b – a)^2/12) = sqrt(33.33333) = 5.773503

Standard deviation = 5.77