Question

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean

μ = 115

and standard deviation

σ = 18.

(a) Calculate the z-scores for the male systolic blood pressures 110 and 120 millimeters. (Round your answers to two decimal places.)

110 mm	z	=
120 mm	z	=

(b) If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 110 and 120 millimeters, what would you say to him? (Enter your numerical answer to the nearest whole number.)

He is (correct or incorrect ) because 2.5 standard deviations below the mean would give him a blood pressure reading of _____ millimeters, which is ( in / below / above) the range of 110to 120 millimeters

Answer 1

Solution:

Given, the Normal distribution with,

   = 115

= 18

a) To find the z score

Formula: z score =

When x = 110 ,z score = (110 - 115)/18 = -0.277777 = -0.28

When x = 120, z score = (120 - 115)/18 = 0.277777 = 0.28

b)The observation which is 2.5 standard deviations below the mean = Mean - (2.5* S.D.)

= 115 - (2.5 * 18)

= 70

So, he is incorrect..because 2.5 standard deviations below the mean would give him a blood pressure reading of 70 millimeters, which is below the range of 110 to 120 millimeters