Question

a) The percentage of adults who have at some point in their life been told that they have hypertension is 23.53%. In a sample of 10 adults, let X be the number who have been told that they have hypertension. Consider the following probability distribution for X. x P(x) 0 ? 1 ? 2 ? 3 ? 4 ? 5 a 6 0.0122 7 0.0021 8 0.0002 9 0.0000 10 0.0000 Find the missing entry that is labelled as 'a'. (answer to 4 decimals)

(b)

[2 marks] Suppose that a group of 10 adults are randomly selected, and 6 of them have been told that they have hypertension. Is this a significantly high number that would suggest that the given percentage of adults who have been told that they have hypertension (i.e., 23.53%) is not correct? (A) Yes, because 0.0122 is less than .05. (B) No, because 0.0122 is less than .05. (C) No, because 6 a not a lot more than expected. (D) No, because 0.0145 is less than .05. (E) Yes, because 0.0145 is less than .05. (F) No, because 0.0475 is less than .05. (G) Yes, because 6 a lot more than expected. (H) Yes, because 0.0475 is less than .05.

Answer 1

Solution(a)
Given in the question
P(hypertension) = 0.2353
Number of sample = 10
We need to calculate probability that exact 5 adult have hypetension which is labelled as a
Here we will use binomial probability distribution which can be calculated as
P(X=n |N,p) = NCn*(p^n)*((1-p)^(N-n))
P(X=5 | 10, 0.2353) = 10C5*(0.2353)^5 * (1-0.2353)(10-5) = 252 * 0.00072 * 0.2615 = 0.0475
a = 0.0475
Solution(b)
P(X = 6 |10, 0.2353) = 0.0122 from the above table given in question a.
yes, this is significantly high number that would suggest that the given percentage of adults who have been told that they hypoertension because 0.0122 is less than 0.05.
So its correct answer is A.