Question

High blood pressure: A national survey reported that

34%

of adults in a certain country have hypertension (high blood pressure). A sample of

24

adults is studied. Round the answer to at least four decimal places.

Part 1 of 4

(a) What is the probability that exactly

5

of them have hypertension?

The probability that exactly 5 of them have hypertension is .

Part 2 of 4

(b) What is the probability that more than

7

have hypertension?

The probability that more than 7 have hypertension is .

Part 3 of 4

(c) What is the probability that fewer than

3

have hypertension?

The probability that fewer than 3 have hypertension is .

Part 4 of 4

(d) Would it be unusual if more than

9

of them have hypertension?

It ▼(Choose one) be unusual if more than 9 of them have hypertension since the probability is .

Answer 1

This is a binomial experiment where the person can either have hypertension or they wouldn't.

(n = 24 ,p = 0.34 = 34% )

P( X =x) =

                = 24Cx * 0.34^x * 0.66^(24-x)

Then we simply subsitutie 'x' every time we need to find the probability for a given 'x'.

X	P(X)
0	0.0000
1	0.0006
2	0.0034
3	0.0129
4	0.0349
5	0.0720
6	0.1174
7	0.1555
8	0.1703
9	0.1559
10	0.1205
11	0.0790
12	0.0441
13	0.0210
14	0.0085
15	0.0029
16	0.0008
17	0.0002
18	0.0000
19	0.0000
20	0.0000
21	0.0000
22	0.0000
23	0.0000
24	0.0000
Total	1.0000

(a) What is the probability that exactly 5 of them have hypertension?

P( X = 5) = 24C5 * 0.34⁵ * 0.66^(24-5)

Ans: 0.0720

Part 2 of 4

(b) What is the probability that more than 7 have hypertension?

P(X > 7) = P( X = 8) + P( X =9)+ ....P( X = 24)

Or using the total probability rule we have

P( X> 7) = 1- [P(X <= 7)]

=1 - [P(X=0) + P( X =1) +......P( X =7)]

=1 - 0.3968

Ans: 0.6032

Part 3 of 4

(c) What is the probability that fewer than 3 have hypertension?

P( X < 3) = P( X <= 2)

=P( X = 0) + P( X = 1) + P( X =2)

Ans: 0.004

Part 4 of 4

(d) Would it be unusual if more than 9 of them have hypertension?

P( X > 9) = 1- P( X <= 9)

=1 - [P( X =0) ..........+ P( X = 9)]

= 1 - 0.7230

=0.277

> 0.05

This is not unusual since p > 0.05​​​​​​​