Mathematics, 11.07.2021 07:40 nicolemaefahey

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed. a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?

Answers: 2

Show answers

Answers

Answer from: leannamat2106

a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

This means that $\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the p-value of Z when X = 135, so:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{135 - 128}{23}$

Z = 0.3

Z = 0.3 has a p-value of 0.6179.

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the p-value of Z when X = 141, so:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{141 - 128}{23}$

Z = 0.565

Z = 0.565 has a p-value of 0.7140.

0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:

X = 125

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{125 - 128}{23}$

Z = -0.13

Z = -0.13 has a p-value of 0.4483.

X = 120

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{120 - 128}{23}$

Z = -0.35

Z = -0.35 has a p-value of 0.3632.

0.4483 - 0.3632 = 0.0851

0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From item b, when X = 135, Z = 0.3.

Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 128}{23}$

X - 128 = 1.28*23

X = 157.44

90% of all people in China have a blood pressure of less than 157.44 mmHg.

Answer from: Quest

Fgfbekbkdbe i appreciate it very much

Answer from: Quest

The surface area would be 576 because you multiply all the numbers then multiply that number by 6
Someone this is overdue and i need to do it

Another question on Mathematics

Mathematics, 21.06.2019 16:00

To make a monster appear large in a movie, a human actor wore a costume and walked through a scale model of a city. the scale used was 1 inch = 15 feet. the actor is 60 inches tall. how tall does the monster appear in the movie? question 5 options: 720 feet 75 feet 4 feet 900 feet

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Which of the functions graphed below has a removable discontinuity?

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Thanh and her crew are building a stage in the shape of a trapezoid for an upcoming festival. the lengths of the parallel sides of the trapezoid are 14 ft and 24 ft. the height of the trapezoid is 12 ft.what is the area of the stage? enter your answer in the box. ft²

Answers: 2

Answer

You know the right answer?

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a s...

Questions