Respuesta :
Answer:
a) [tex]Z = -2.7[/tex]
b) [tex]Z = 2.3[/tex]
c) Kyle's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.
d) [tex]X = 144.5[/tex]
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 127, \sigma = 10[/tex]
(a) 100 millimeters z-score =
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 127}{10}[/tex]
[tex]Z = -2.7[/tex]
(b) 150 millimeters z-score =
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 127}{10}[/tex]
[tex]Z = 2.3[/tex]
(c) Kyle's doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of his score?
1.75 standard deviations above the mean systolic blood pressure of males.
The problem does not talk about age.
So the answer is:
Kyle's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.
d) Calculate Kyle's blood pressure
This is X when Z = 1.75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 127}{10}[/tex]
[tex]X - 127 = 1.75*10[/tex]
[tex]X = 144.5[/tex]
