Question

For males in a certain town, the systolic blood pressure is normally distributed with a mean of and a standard deviation of 8. If 428 males from the town are randomly selected to participate in a study, how many of them would be expected to have a systolic blood pressure higher than 114, to the nearest whole number?

Answer 1

In a group of 428 males in the town, the number of males expected to have a systolic blood pressure higher than 114 is 331.

Step-by-step explanation

To answer this, we need to first obtain the probability of a male person having a systolic blood pressure higher than 114.

Since it is a normal distribution, we will used the normal distribution tables to obtain the probability after standardizing the score.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ

x = The value = 114

μ = Mean = 120

σ = Standard deviation = 8

z = (x - μ)/σ

z = (114 - 120)/8 = (-6/8) = -0.75

P(x > 114) = P(z > -0.75)

= 1 - P(z ≤ -0.75)

= 1 - 0.227

= 0.773

So,

Probability of a male person having systolic blood pressure higher than 114 = 0.773

In a group of 428 males, we now need to find the expected number of people that will have a systolic blood pressure higher than 114.

Expected value = np

n = Number of variables = 428 males

p = Probability = 0.773

Expected value = np = (428) (0.773) = 330.8 = 331 to the nearest whole number.

Hope this Helps!!!