Respuesta :
Answer:
(1) The value of X is, 151.13.
This score X, is the 95th percentile of systolic blood pressure scores among women. The percentile rank of this score is 95.
(2) The percentage of women have systolic blood pressure in the range 140 to 159 is 9.01%.
(3) The percentage of women having systolic blood pressure below 90 is 21.19%.
Step-by-step explanation:
The random variable X is defined as the systolic blood pressure of women.
The distribution of X is, N (110, 25²).
(1)
The value of z-score that is in the bottom 95% is, 1.645.
Compute the value of X as follows:
[tex]z=\frac{X-\mu}{\sigma}\\1.645=\frac{X-110}{25}\\X=110+(1.645\times 25)\\X=151.125\\\approx151.13[/tex]
The value of X is, 151.13.
This score X, is the 95th percentile of systolic blood pressure scores among women. The percentile rank of this score is 95.
(2)
Compute the probability of X between 140 and 159 as follows:
[tex]P(140<X<159)=P(\frac{140-110}{25}<\frac{X-\mu}{\sigma}<\frac{159-110}{25})\\=P(1.20<Z<1.96)\\=P(Z<1.96)-P(Z<1.20)\\=0.9750-0.8849\\=0.0901[/tex]
The percentage of systolic blood pressure between 140 and 159 is,
0.0901 × 100 = 9.01%
Thus, the percentage of women have systolic blood pressure in the range 140 to 159 is 9.01%.
(3)
Compute the probability of X below 90 as follows:
[tex]P(X<90)=P(\frac{X-\mu}{\sigma}<\frac{90-110}{25})\\=P(Z<-0.80)\\=1-P(Z<0.80)\\=1-0.7881\\=0.2119[/tex]
The percentage of women having systolic blood pressure below 90 is,
0.2119 × 100 = 21.19%.
Thus, the percentage of women having systolic blood pressure below 90 is 21.19%.
