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.)

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.)

𝜇 = 6; 𝜎 = 2

P(5 ≤ x ≤ 9) = 

Answer 1

Hi Brandon,

Here we will want to use z scores to find the probability of x<= 9 and x<=5, then we will subtract P(x<=5) from P(x<=9) to find the probability x occurs between these two values

Start by finding the z score for each value

x = 9 , z = (x-μ)/σ = (9-6)/2 = 3/2

x = 5 , z = (x-μ)/σ = (5-6)/2 = -1/2

Then use the z score table to find the probability for each respective z score

P(x<=5) = .3085

P(x<=9)= .9332

Now subtract P(x<=9) - P(x<=5) = .9932 - .3085 = .6847

Answer 2

Calculate the z scores for the x's.

z = x - 𝜇 / 𝜎

for x = 5 - 6 / 2 = -0.5

for x = 9 - 6 / 2 = +1.5

Consult a table of normal distribution values to determine the % area enclosed by the two x values. This would be the probability of the x's being between the two values. Tables vary in the way they are presented, so be sure you are interpreting them correctly.

I got 0.62 as the probability using two different table presentations.