Cancer Survival Rates: Suppose a certain type of cancer has a 0.64 survival rate

Question

Cancer Survival Rates: Suppose a certain type of cancer has a 0.64 survival rate for five years. This means that 64% 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 0.64 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 76 survived (about 54%). 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 76 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 =np=140*0.64=89.6

b)and std deviation =(np(1-p))1/2 =5.679

c)P(X<=76) =P(Z<(76.5-89.6)/5.679)=P(Z<-2.3066) hence z score is -2.3066

d)P(Z<-2.3066) =0.0105

as probability of that is less then 0.05 ; Yes, that is an unusual rate

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.