Question

Researchers are concerned about the prevalence of skin cancers among adults aged 35-50 in a population with frequently moderate, warm temperatures. The prevalence of such skin cancers in the population is only 16%. Suppose a sample of adults in this age range is conducted and among the 197 adults surveyed, 64 reported at least one skin cancer removal.

A) Can researchers approximate the distribution with the standard normal?

B) Calculate the probability of observing the results seen in the sample.

C) What is the probability of observing between 75 and 46 participants in the sample reporting at least one skin cancer?

A) No, npq<5

B) <0.05

C) 0.0245

or

A) Yes, npq>5

B) <0.01

C) 0.1115

or

A) Yes, npq>5

B) <0.0001

C) 0.00245

Answer 1

A.

n = 197

x = 64

Since x and n-x > 10. i.e. we can approximate it with normal distribution.

B.

Probability of a point in the distribution is very low i.e. <0.0001

C.

46/197= 0.2335

75/197 = 0.3807

So,

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