Patients suffering from cancer must often decide whether to have their tumors treated with surgery or with radiation. A factor in their decision is the 5-year survival rates for these treatments. Surprisingly, it has been found that patients decisions often seem to be affected by whether they are told the 5-year survival rates or the 5-year death rates (even though the information content is identical). For instance, in an experiment a group of 200 male prostate cancer patients were randomly divided into two groups of size 100 each. Each member of the first group was told that the 5-year survival rate for those electing surgery was 77 percent, whereas each member of the second group was told that the 5-year death rate for those electing surgery was 23 percent. Both groups were given the same information about radiation therapy. If it resulted that 24 members of the first group and 12 of the second group elected to have surgery, what conclusions would you draw?

Lecture 7: 8.5 General Continuous Random Variables Definition: - A curve (or function) is called a Probability Density Curve if: 1. It lies on or above the horizontal axis. 2. Total area under the curve is equal to 1. - KEY IDEA: AREA under a density curve over a range of values corresponds to the PROBABILITY that the random variable X takes on a value in that range. - The probability that the variable X exactly equals a specified value is 0. - Instead, we find the probability that X could take on values in an interval. 8.6 Normal Random Variables A Normal Curve: Symmetric, bell-‐shaped, centered