For the normal distribution with parameters μ = 3, σ = 2; calculate P(0

Question

For the normal distribution with parameters μ = 3, σ = 2; calculate P(0 < x < 8).
A) 0.3124
B) 0.9270
C) 0.8123
D) 0.6723

Quizplus · Accepted Answer

To calculate $P(0 < x < 8)$ for a normal distribution with $\mu = 3$ and $\sigma = 2$, we first convert the x-values to z-scores using the formula $z = \frac{x - \mu}{\sigma}$. For $x = 0$, $z = \frac{0 - 3}{2} = -1.5$. For $x = 8$, $z = \frac{8 - 3}{2} = 2.5$. Then, we look up these z-scores in a standard normal distribution table or use a calculator. The table gives us the probabilities up to these z-scores. Subtracting the probability at $z = -1.5$ from the probability at $z = 2.5$ gives us the probability of $x$ being between 0 and 8. This calculation yields a probability of approximately 0.9270, indicating that there is a 92.70% chance that $x$ falls between 0 and 8 in this distribution.

For the Normal Distribution with Parameters μ = 3, σ