Answer:
(1) The value of <em>X</em> is, 151.13.
This score X, is the <u>95th</u> percentile of systolic blood pressure scores among women. The percentile rank of this score is <u>95</u>.
(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 <em>X</em> is defined as the systolic blood pressure of women.
The distribution of <em>X</em> is, N (110, 25²).
(1)
The value of <em>z</em>-score that is in the bottom 95% is, 1.645.
Compute the value of <em>X</em> as follows:
The value of <em>X</em> is, 151.13.
This score X, is the <u>95th</u> percentile of systolic blood pressure scores among women. The percentile rank of this score is <u>95</u>.
(2)
Compute the probability of <em>X</em> between 140 and 159 as follows:
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 <em>X</em> below 90 as follows:
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%.