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.

Question

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:

• \( P(X=3) = 0 \)
• \( P(X \leq 7) = 0.2 \)
• \( P(X > 10) = 0.3 \)