2) Plot these points on a piece of graph paper. Draw a line to connect each of the pairs indicated. Then, determine which line i
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Answer:
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 and standard deviation
, the z-score of a measure X is given by:
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
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:
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:
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
has a p-value of 0.4483.
X = 120
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.
90% of all people in China have a blood pressure of less than 157.44 mmHg.