The waiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function f(x) = 0.5exp(−0.5x) for 0 < x. Determine the following:

a. P(X < 0.5)
b. P(X > 2)
c. Value x (in hours) exceeded with probability 0.05.

The value of P(X < 0.5)  is 0.22.

The value of P(x>2) is 0.32.

The value of x is 5.991 hours exceeded probability 0.05.

Given that,

The waiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function;

We have to determine,

The value of P(X < 0.5)  and  P(X > 2).

The value x (in hours) exceeded probability 0.05.

According to the question,

1. The value of P(X < 0.5)  is determined by integration of the function,

The value of P(X < 0.5)  is 0.22.

2.  The value of P(X > 2 ) is determined by integration of the function,

The value of P(x>2) is 0.32.

3. The value of x (in hours) exceeded probability 0.05.

The value of x is 5.991 hours exceeded probability 0.05.

For more details refer to the link given below.

link

The value  6 hours exceeded with probability 0.05.

Step-by-step explanation:

We are given that The waiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function

for x>0

a. P(X < 0.5)

b. P(X > 2)

c. Value x (in hours) exceeded with probability 0.05.

P(X>x)=0.05

The value  6 hours exceeded with probability 0.05.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

the answer is 13 cm