Problem:

11 .Uses information from the empirical rule.Visualize the normal distribution.The area under the curve from z = 0 to z =+1 is .34. The area from -1 to +1 is 68% per the empirical rule. This is the probability that z is greater than 0 but less than +1.The probability that z is greater than 0 is .50. Thus the probability of a z value larger than z = +1 is .50 - .34 = .16. This is the same as the probability of a value larger than one standard deviation above the mean. Remember that z = +1 is one standard deviation higher than the mean. What about z = -1? That is one standard deviation below the mean.

MY ANSWER:

Hello Class!

11. Uses information from the empirical rule.Visualize the normal distribution.The area under the curve from z = 0 to z =+1 is .34. The area from -1 to +1 is 68% per the empirical rule. This is the probability that z is greater than 0 but less than +1.The probability that z is greater than 0 is .50. Thus, the probability of a z value larger than z = +1 is .50 - .34 = .16. This is the same as the probability of a value larger than one standard deviation above the mean. Remember that z = +1 is one standard deviation higher than the mean.

What about z = -1? That is one standard deviation below the mean.

Related to the value of z=-1:

Z is less than -1: Since the normal distribution is symmetric, the probability that z is less than -1 is the same as the probability that z is greater than +1: [ P(z < -1) = P(z > +1) = 0.16 ].

This means that 16% of the data lies more than one standard deviation below the mean.

Thank you, Class!

Professor's answer:

Pleased you looked back at your answers and are interpreting the answer. Remember that sometimes there is more than one way to solve a problem, but the answer should always be the same.

How we interpret the answer? Thank you!