Question

If X has a normal distribution with mean = 5 and standard deviation = 2, find Pr(2 less than or equal to X and is greater than or equal to 6)

Answer 1

To find Pr(2< = X < = 6) in a normal distribution with mean = 5 and standard deviation = 2, we calculate the z-scores for the values of 2 and 6 and use the standard normal distribution table or a calculator to find the area between these z-scores.

Step-by-step explanation:

To find Pr(2<=X<=6), we need to calculate the area under the normal curve between the values of 2 and 6. Since X has a normal distribution with mean = 5 and standard deviation = 2, we can convert these values to z-scores using the formula z = (X - mean) / standard deviation.

For X = 2, the z-score is (2 - 5) / 2 = -1.5. For X = 6, the z-score is (6 - 5) / 2 = 0.5.

We can then use the standard normal distribution table or a calculator to find the area between -1.5 and 0.5, which represents Pr(2<=X<=6).