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

Question

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

𝜇 = 8; 𝜎 = 2

P(7 ≤ x ≤ 10) = 

Answer 1

We can calculate the probability by "standardizing" the described distribution, and referring to the standard normal distribution table.

z = (x - µ)/σ, where z is our standardized score.

Note: P(7 < x < 10) = P(x > 7) - P(x > 10)

P(x > 7) = P((x - µ)/σ > (7 - 8)/2) = P(z > -0.5)

Based on the standard normal distribution table, P(z > -0.5) = 0.6915

P(x > 10) = P((x - µ)/σ > (10 - 8)/2) = P(z > 1) = 0.1587

Again, the calculation is based on a reference to the standard normal distribution table.

P(7 < x < 10) = P(x > 7) - P(x > 10) = 0.6915 - 0.1587 = 0.5328

I hope this helps! Please let me know of any questions.