Respuesta :
Answer:
(a) The probability distribution table is provided in the attachment.
(b) The probability distribution of X is discrete.
(c) The probability a service call will take 3 hours is 0.30.
(d) The probability that the service technician will have to work overtime is 0.70.
Step-by-step explanation:
Let X = number of hours a service calls take.
(a)
The probability of an event E is:
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = number of favorable outcomes
N = total number of outcomes.
The probability distribution table is provided in the attachment.
(b)
For a discrete probability distribution:
- [tex]f(x) \geq 0\\[/tex]
- [tex]\sum f(x)=1[/tex]
Check that the probability distribution of X is discrete as follows:
The value of f (x) for all values of x is greater than 0.
The sum of all f (x) is 1.
Thus, the probability distribution of X is discrete.
(c)
The probability of X = 3 is:
[tex]P(X=3) = f(3) = 0.30[/tex]
Thus, the probability a service call will take 3 hours is 0.30.
(d)
The service technician has 2 hours (3:00 PM to 5:00 PM) to fix the machine.
Compute the probability that the service technician will have to work overtime as follows:
P (X > 2) = P (X = 3) + P (X = 4)
[tex]=0.30+0.40\\=0.70[/tex]
Thus, the probability that the service technician will have to work overtime is 0.70.
