Question

1a) Qualifying Test Scores To qualify for a medical study, an applicant must have a systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 3, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to one decimal place.Applicants must have a lower blood pressure limit of ___ and an upper blood pressure limit of ____to qualify for the study.

Answer 1

Given in the question:

a.) mean = μ = 120

b.) standard deviation = σ = 3

The z - distribution of the 60% is therefore,

P( -z < Z < z ) = 0.60

P( Z < z ) - P( Z < -z ) = 0.60

2*P(Z < z ) - 1 = 0.60

2*P(Z < z ) = 1 + 0.60

P( Z < z ) = 1.60 / 2

P( Z < z ) = 0.80

P( Z < -0.84) = 0.80

Therefore, z = -0.84 and z = 0.84

Using z - score formula:

X = +/-z * σ + μ

At, X = -z * σ + μ

= -0.84 * 4 + 120

= 116.6

At X = +z * σ + μ

= 0.84 * 4 + 120

= 123.4

Therefore,

Lower blood pressure limit = 116.6

Upper blood pressure limit = 123.4