Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)P(50 ? x ? 70)

? = 42; ? = 15

Answer 1

P(50 ≤ x ≤ 70) = 0.3085

This probability is calculated using the normal distribution with a mean (μ) of 42 and a standard deviation (σ) of 15.

Step-by-step explanation:

To find the probability P(50 ≤ x ≤ 70) with a normal distribution where the mean (μ) is 42 and the standard deviation (σ) is 15, the calculated probability is 0.3085 when rounded to four decimal places.

In a normal distribution, probabilities between specific values are determined by calculating the area under the curve within that range.

Using the z-score formula and standard normal distribution tables, we can convert the given values of x to z-scores and find the corresponding probabilities. In this case, the calculated probability reflects the likelihood of x falling between 50 and 70.