Given that x is a normally distributed random variable with a mean of 60 and a standard deviation of 10, find the P(56 < x <74). Please show all your work and write your answer in a complete sentence.
Using the information from question 1, what percentage of the population will have an "x" value greater than 56 orP(x>56.)Please write your answer in a complete sentence.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to your Z scores.
To find the probability P(56 < x < 74), we need to first standardize the values. We can do this by calculating the z-scores for each value.
The z-score is calculated as (x - mean) / standard deviation.
For 56, the z-score is (56 - 60) / 10 = -0.4.
For 74, the z-score is (74 - 60) / 10 = 1.4.
Next, we look up the corresponding probabilities using the standard normal distribution table or a calculator.
From the z-table, we find that the area to the left of -0.4 is 0.3446 and the area to the left of 1.4 is 0.9192.
To find the probability of the interval 56 < x < 74, we subtract the smaller area from the larger area: 0.9192 - 0.3446 = 0.5746.
Therefore, the probability P(56 < x < 74) is approximately 0.5746.
For the second question, we want to find the percentage of the population that will have an "x" value greater than 56 or P(x > 56).
Using the standard normal distribution table or a calculator, we find the area to the left of -0.4 is 0.3446.
To find the probability to the right of -0.4, we subtract the left area from 1: 1 - 0.3446 = 0.6554.
Therefore, the percentage of the population that will have an "x" value greater than 56 is approximately 0.6554 or 65.54%.