Cancer Survival Rates: Suppose a certain type of cancer has a 0.77 survival rate

Question

Cancer Survival Rates: Suppose a certain type of cancer has a 0.77 survival rate for five years. This means that 77% of those diagnosed with this type of cancer have survived at least 5 years (those that die from something else in that time are excluded). Now, suppose you check on 140 people with this type of cancer 5 years after diagnosis and treatment from a particular hospital. (a) Assume the 0.77 survival rate is accurate. In randomly selected groups of 140 people diagnosed with this type of cancer, what is the mean number of survivors at the five-year mark? Round your answer to one decimal place. = (b) What is the standard deviation? Round your answer to one decimal place. = (c) You check on 140 such patients from a certain hospital and find that only 95 survived (about 68%). With respect to the mean and standard deviation found in parts (a) & (b) respectively, what is the z-score for this many survivors? Round your answer to two decimal places. z = (d) While the survival rate at this particular hospital is below the national average, is 95 out of 140 low enough to be considered unusual? Yes, that is an unusual rate. No, it is not low enough to be considered unusual.

Explanation / Answer

(a) Mean number of surviovors after 5 years mark = 140 * 0.77 = 107.8

(b) standerd deviation = sqrt( n* p * (1-p) ) = sqrt ( 140 * 0.77 * 0.23) = 5.0

(C) on;y 95 people have survive

Z score of the survors = (x - )/ = ( 98 - 107.8) / 5.0 = -1.96

(d) for 95 out of 140 , Z value will be = (95 - 107.8)/5.0 = -2.56

so for having 95 or less survivors out of 140 comes have probability only 0.0052 that means it have only 0.52 % chance .and it is under 1% significance level.

So, yes this is an unusual rate.

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