Question

Any normal distribution is a continuous distribution and as such it has the property that the probability of any specific number is always zero, for example P(X=5)=0, P(X=-2)=0.

Find P(X=3)=

If P(X<7)=0.2, then P(X≤7)=

If P(X≥10)=0.3 then P(X>10)=

Answer 1

In a continuous distribution, the probability of any specific value (i.e., a single point) is always zero. Therefore:

1. **Probability of a specific value:**
\[
P(X=3) = 0
\]

2. **Probability of being less than or equal to a value:**
If \( P(X < 7) = 0.2 \), then:
\[
P(X \leq 7) = P(X < 7) + P(X = 7) = 0.2 + 0 = 0.2
\]
(since \( P(X = 7) = 0 \) in a continuous distribution).

3. **Probability of being greater than a value:**
If \( P(X \geq 10) = 0.3 \), then:
\[
P(X > 10) = P(X \geq 10) - P(X = 10) = 0.3 - 0 = 0.3
\]
(for the same reason: \( P(X = 10) = 0 \)).

To summarize:
- \( P(X=3) = 0 \)
- \( P(X \leq 7) = 0.2 \)
- \( P(X > 10) = 0.3 \)