Question

a. The systolic blood pressure (given in millimeters) of females has an approximately normal distribution with mean μ = 122 millimeters and standard deviation σ = 16 millimeters. Systolic blood pressure for females follows a normal distribution. Calculate the z-scores for a female systolic blood pressure of 136 millimeters (Round answer to 3 decimal places).

b. The systolic blood pressure (given in millimeters) of females has an approximately normal distribution with mean μ = 122 millimeters and standard deviation σ = 16 millimeters. Systolic blood pressure for females follows a normal distribution. What is the probability that a female’s systolic blood pressure is between 110 and 135 millimeters? Round answer to 3 decimal places (i.e. 0.123)

c. The systolic blood pressure (given in millimeters) of females has an approximately normal distribution with mean μ = 122 millimeters and standard deviation σ = 16 millimeters. Systolic blood pressure for females follows a normal distribution. What is the probability that a female’s systolic blood pressure is less than 90 millimeters? Round answer to 3 decimal places (i.e. 0.123)

Answer 1

Solution :

Given that ,

mean = = 122

standard deviation = = 16

(a)

x = 136

z = (x - ) / = (136 - 122) / 16 = 0.875

(b)

P(110 < x < 135) = P[(110 - 122)/ 16) < (x - ) /  < (135 - 122) / 16) ]

= P(-0.75 < z < 0.8125)

= P(z < 0.8125) - P(z < -0.75)

= 0.7917 - 0.2266

= 0.565

(c)

P(x < 90) = P[(x - ) / < (90 - 122) / 16]

= P(z < -2)

= 0.023