Question

Let X be normally distributed with mean μ = 18 and standarddeviation σ = 14. Find P(18 ≤ X ≤ 25). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

To find P(18 ≤ X ≤ 25), calculate the z-scores for both x-values and use the standard normal distribution table. The probability is approximately 0.6915.

Step-by-step explanation:

To find P(18 ≤ X ≤ 25), we need to calculate the z-scores for both x-values and use the standard normal distribution table.

1. Calculate the z-score for x = 18: z = (18 - μ) / σ = (18 - 18) / 14 = 0
2. Calculate the z-score for x = 25: z = (25 - μ) / σ = (25 - 18) / 14 = 0.5
3. Using the standard normal distribution table, find the area to the left of z = 0.5, which is 0.6915.
4. Since we want the probability between 18 and 25, we subtract the area to the left of z = 0 from the area to the left of z = 0.5: P(18 ≤ X ≤ 25) = 0.6915 - 0 = 0.6915

Therefore, P(18 ≤ X ≤ 25) is approximately 0.6915.