Question

4. Breast cancer occurs most frequently among older women, Of all age groups, women in their 60s have the highest rate of breast cancer. It is estimated that 3.7% of women in their 60s get breast cancer. Mammograms are X-ray images of the breast used to detect breast cancer. A mammogram can typically identify correctly 84.9% of cancer cases (sensitivity 84.9%) and 95.13% of cases without cancer (specificity = 95%). (This is exactly like problem #11) First write down the probabilities given in the question and then answer the following questions a. b. Sally who is in her 60s gets a mammogram. What is the probability that she will test positive for breast cancer? c. Suppose Sally tests positive for breast cancer, what is the probability that she actually has the cancer? 5. Bigger mammals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and standard deviation 3 days. = 0 = X-is What percent of horse pregnancies are longer than 339 days?

Answer 1

5.

Sol:

We are given that : The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and standard deviation 3 days.

That is : Mean = $\mu =336$ and Standard Deviation = $\sigma =3$

339 is above mean = 336 , hence find k such that :

Mean + k*SD = 339

336 + k* 3 = 339

336 - 336 + k*3 = 339 -336

k*3 = 3

k = 3/3

k = 1

Thus 339 is one standard deviation above mean value.

Thus according to empirical rule , 68% of the data fall within 1 standard deviation from mean.

So 100 - 68 = 32% of the data fall outside of the 1 standard deviation from mean value.

So half of 32% will be above   339

That is : 32% /2 = 16% of horse pregnancies are longer than 339 days

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