Question

that has a ton hatibution with the specified mean and standard deviation. Find the indicated probability (Koond your answer to four decimal places) P( 3 **5,0)= Box

Answer 1

The indicated probability
`\( P(3 \leq X \leq 5) \)` for a normal distribution with a specified mean and standard deviation is determined by finding the z-scores for 3 and 5, and then using a standard normal distribution table. The final calculated probability is rounded to four decimal places.

Step-by-step explanation:

To find
`\( P(3 \leq X \leq 5) \),` we first need to standardize the values using the z-score formula:
`\( Z = \frac{{X - \mu}}{{\sigma}} \)`, where
`\( X \)` is the value,
`\( \mu \)` is the mean, and
`\( \sigma \)` is the standard deviation. Assuming a standard normal distribution, we find the z-scores for 3 and 5.

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores. This area represents the probability
`\( P(3 \leq X \leq 5) \)` for a standard normal distribution.

The final probability is rounded to four decimal places for precision. This process ensures an accurate representation of the likelihood of the random variable falling between 3 and 5 in a standard normal distribution.

In summary, the solution involves standardizing the values, determining the corresponding z-scores, and then finding the probability in the standard normal distribution table. Rounding the result to four decimal places provides a concise and precise representation of the indicated probability.