Question

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 4, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate z value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of 116.64 and an upper blood pressure limit of 120.34] to qualify for the study. X 5

Answer 1

Solution:

Given that,

mean = μ = 120

standard deviation = σ = 4

The z - distribution of the 60% is,

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

z = -0.84

and

z = 0.84

Using z - score formula,

X = z * σ +  μ

= -0.84 * 4 + 120  

= 116.6

and

X = z * σ +  μ

= 0.84 * 4 + 120  

= 123.4

Lower blood pressure limit = 116.6

Upper blood pressure limit = 123.4

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