Question

A normal random variable X has an unknown mean and standard deviation σ = 2. If the probability that X exceeds 7.5 is 0.8023, find μ.

Answer 1

To find the mean µ, we can use the z-score formula. The probability that X exceeds 7.5 is 0.8023, which means the probability that X is less than or equal to 7.5 is 0.1977 (1 - 0.8023). Using the z-score formula, we can find the z-score corresponding to a probability of 0.1977.

Step-by-step explanation:

To find the mean µ, we can use the z-score formula. The probability that X exceeds 7.5 is 0.8023, which means the probability that X is less than or equal to 7.5 is 0.1977 (1 - 0.8023). Using the z-score formula, we can find the z-score corresponding to a probability of 0.1977.

z = (X - µ) / σ

0.1977 = (7.5 - µ) / 2

After solving for µ, we find that µ is equal to 4.8.