Respuesta :
Using the normal distribution, it is found that 84 people would be expected to have BP > 160.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
1 - 0.9582 = 0.0418.
Out of 2000 people:
0.0418 x 2000 = 83.6.
Rounding to the nearest integer, 84 people would be expected to have BP > 160.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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