Answer :
Answer:
For a continuous random variable X, P(20 ≤ X ≤ 40) = 0.15 and P(X > 40) = 0.16.
Step-by-step explanation:
Here, P(x > 40) = 0.16
a). P(x < 40) = 1 - P(x > 40)
= 1 - 0.16
= 0.84
b). P(x < 20) = 1 - [tex]P(x\geq 20)[/tex]
= 1 - {P(20 ≤ X ≤ 40) + P(X > 40)}
= 1 - (0.15 + 0.16 )
= 1 - 0.31
= 0. 69
c). P(x = 40) = 0; The probability that a continuous variable assume a particular value is zero.
Probabilities are used to determine the chances of an event.
The probabilities are:
- [tex]\mathbf{P(x < 40) = 0.84}[/tex]
- [tex]\mathbf{P(x < 20) = 0.69}[/tex]
- [tex]\mathbf{P(x = 40) = 0}[/tex]
The given parameters are:
[tex]\mathbf{P(20 \le x \le 40) = 0.15}[/tex]
[tex]\mathbf{P(x > 40) = 0.16}[/tex]
(a) P (X < 40)
To do this, we make use of the following compliment rule.
[tex]\mathbf{P(x < 40) = 1 - P(x > 40) - P(x = 40)}[/tex]
Because the probability is continuous, then:
[tex]\mathbf{P(x = 40) = 0}[/tex]
So, we have=:
[tex]\mathbf{P(x < 40) = 1 - 0.16 - 0}[/tex]
[tex]\mathbf{P(x < 40) = 0.84}[/tex]
(b) P (X < 20)
To do this, we make use of the following compliment rule.
[tex]\mathbf{P(x < 20) = 1 - P(20 \le x \le 40) - P(x > 40)}[/tex]
So, we have=:
[tex]\mathbf{P(x < 20) = 1 - 0.15 - 0.16}[/tex]
[tex]\mathbf{P(x < 20) = 0.69}[/tex]
(c) P(x = 40)
In (a), we have:
[tex]\mathbf{P(x = 40) = 0}[/tex]
Read more about probabilities at:
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