Question

Suppose 49% of the doctors in America are dentists. If a random sample of size 689 is selected, what is the probability that the proportion of doctors who are dentists will be less than 47%

Answer 1

`P(<47\%)=0.1468`

Explanation:

From the question we are told that:

Percentage of Dentist Doctors P(D)=49\%

Sample size n=689

Generally the equation for probability that the proportion of doctors who are dentists will be less than
`P(<47\%)` is mathematically given by

`P(<47\%)=Z>(\frac{\=x-P(D)}{\sqrt{(P(D)*1-P(D))/(n)}})`

`P(<47\%)=Z>(\frac{0.47-0.49}{\sqrt{(0.49*0.51)/(689)}})`

`P(<47\%)=Z>(1.05)`

Therefore from table

`P(<47\%)=0.1468`