Suppose a normal distribution has a mean of 50 and a standard deviation of 3. What is P(x ≤ 47)?A.0.84B.0.975C.0.16D.0.025SUBMITarrow_backPREVIOUS

1. Break Down the Problem

To find $P(x \leq 47)$ for a normal distribution with mean $\mu = 50$ and standard deviation $\sigma = 3$, we need to calculate the z-score for $x = 47$.

2. Relevant Concepts

The z-score can be calculated using the formula: $z = \frac{x - \mu}{\sigma}$ where:

• $x$ is the value for which we want to find the probability,
• $\mu$ is the mean of the distribution,
• $\sigma$ is the standard deviation.

3. Analysis and Detail

1. Calculate the z-score for $x = 47$: $z = \frac{47 - 50}{3} = \frac{-3}{3} = -1$

2. Now, we need to find $P(z \leq -1)$. Using the standard normal distribution table, we can find this probability.

4. Verify and Summarize

From z-tables, the probability $P(z \leq -1)$ corresponds to approximately $0.1587$. This means: $P(x \leq 47) = 0.1587$

Final Answer

Thus, the closest answer choice is: C. 0.16