1. Cancer Survival Rates: Suppose a certain type of cancer has a 0.75 survival r

Question

1. Cancer Survival Rates: Suppose a certain type of cancer has a 0.75 survival rate for five years. This means that 75% 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 130 people with this type of cancer 5 years after diagnosis and treatment from a particular hospital.

(a) Assume the 0.75 survival rate is accurate. In randomly selected groups of 130 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 130 such patients from a certain hospital and find that only 91 survived (about 70%). 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 91 out of 130 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 ) =130 * 0.75 = 97.5
b.
Standard Deviation ( npq )= 130*0.75*0.25 = 4.9371
c.
P(X < 91) = (91-97.5)/4.9371
= -6.5/4.9371= -1.3166              
d.
P(X < 91) = (91-97.5)/4.9371
= -6.5/4.9371= -1.3166
= P ( Z <-1.3166) From Standard Normal Table
= 0.094                  
result is > 0.05 and we conclude, No, it is not low enough to be considered unusual

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