In a recent year, the American Cancer said that the five-year survival rate for new cases of stage 1 kidney cancer is 95%. You randomly select 12 men who were new stage 1 kidney cancer cases this year and calculate their five-year survival rate. 1) Can you use the normal distribution to approximate the binomial distribution? 2) If you can, what are the mean and standard deviations? If not, why not? A survey indicates that 59% of men purchased perfume in the past year. You randomly select 15 men and ask them if they have purchased perfume in the past year. 3) Can you use the normal distribution to approximate the binomial distribution? 4) If you can, what are the mean and standard deviations? If not, why not? 5) What is the probability that the number of men who purchased perfume in the past year is more than 10?

In a recent year, the American Cancer said that the five-year survival rate for new cases of stage 1 kidney cancer is 95%. You randomly select 12 men who were new stage 1 kidney cancer cases this year and calculate their five-year survival rate. 1) Can you use the normal distribution to approximate the binomial distribution? NO 2) If you can, what are the mean and standard deviations? If not, why not? 𝑛𝑞<5 A survey indicates that 59% of men purchased perfume in the past year. You randomly select 15 men and ask them if they have purchased perfume in the past year. 3) Can you use the normal distribution to approximate the binomial distribution? YES (𝑛𝑝= .59 15 =8.85;𝑛𝑞= .41 15 =6.15) 4) If you can, what are the mean and standard deviations? If not, why not? 𝜇=𝑛𝑝= .59 15 =8.85 𝜎= 𝑛𝑝𝑞 = 15 (.59)(.41) ≈1.905

5) What is the probability that the number of men who purchased perfume in the past year is more than 10? Remember to correct for continuity!! We are using the normal distribution, which is a continuous distribution, to answer a binomial question, which has discrete data. We need to add half a unit to the upper end and/or subtract half a unit from the lower end. In this case, we are going up toward positive infinity, so our number will be the low end. The smallest number more than 10 is 11, so subtract .5 from 11 We will go from 10.5 to infinity.

2nd VARS 3 (1 - .193, 8.85, 1.905) = 10.501, so it checks. 5) What is the probability that the number of men who purchased perfume in the past year is more than 10? 8.85 10.755 12.66 14.565 3.135 5.04 6.945 .500 .841 .159 .977 .023 .9985 ≈0.00 ≈1.00 .0015 Looking at the curve, our answer should be between .159 and .500, closer to .159. 2nd VARS 2 10.5, 1𝐸99, 8.85. 1.905 =.193 This matches our prediction of between .159 and .500 and closer to .159. 2nd VARS 3 (1 - .193, 8.85, 1.905) = 10.501, so it checks.