Question

Homework: Week #6( sec. 6.1,6.2, 6.4) | 11 of 20 (8 complete) > Score: 0 of 1 pt 6.4.29 A random variable follows the continuous uniform distribution between 20 and 50. a. Calculate the following probabilities below for the distribution. 1. P(x 35) 2. P(x 530) 3. P(x540) 4. P(x=32) b. What are the mean and standard deviation of this distribution? a. 1. P(x 5 35) = (Type an integer or decimal rounded to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. 5 parts remaining Clear All

Answer 1

6.4.29

UNIFORM DISTRIBUTION
PDF of uniform distribution f(x) = 1 / ( b - a ) for a < x < b
b = maximum Value
a = minimum Value
f(x) = 1/(b-a) = 1 / (50-20) = 1 / 30 = 0.0333
I.
mean = a + b / 2
=(20+50)/2
=35
II.
standard deviation = sqrt ( ( b - a ) ^ 2 / 12 )
=sqrt(50-20)^2 / 12
=8.6603

a.
1.
P(X > 35) = (50-35) * f(x)
= 15*0.0333
= 0.5
p(X<=35) = 1-p(X>35)
p(X<=35) = 1-0.5 = 0.5

2.
P(X > 30) = (50-30) * f(x)
= 20*0.0333
= 0.6667
p(X<=30) = 1-p(X>30)
p(X<=30) = 1-0.6667
p(X<=30) = 0.333

3.
P(X > 40) = (50-40) * f(x)
= 10*0.0333
= 0.3333
p(X<=40) = 1-p(X>40)
p(X<=40) = 1-0.3333
p(X<=40) = 0.666

4.
P(X <= 32) = (32-20) * f(x)
= 12*0.0333
= 0.4
Answers:
a.
1.
p(X<=35) = 0.5
b.
mean = 35
standard deviation =8.66