Question

The systolic arterial blood pressure observed for 20 dogs is normally distributed with a mean of 152 mm of mercury (hg) and a standard deviation of 18 mm of hg. what is the probability that the systolic arterial blood pressure is 100 mm of hg

Answer 1

Given: The systolic arterial blood pressure observed for 20 dogs is normally distributed with a mean of 152 mm of mercury (Hg) and a standard deviation of 18 mm of Hg.  

To find: P(100 < 152)

Method: Calculation of Z-Score followed by the probability or area of the bell curve at X = 100.

Solution:

Mean u = 152, std s = 18

Z score = $\frac{X-u}{s} = \frac{100-152}{18} = -2.89$

The value of P(100<152) is calculated by looking at the value of Z in the Z score for the standard normal distribution given in the image.

P(Z=-2.89) = 0.0019

The P(Z = -2.89) corresponds to the area in the left tail of the bell curve.

Thus the probability of 100 mm Hg blood pressure is 0.0019.