QuestionIn a town, 105 males are selected. With a mean of 130 and SD of 10, how many have systolic BP < 154?
Studdy Solution
STEP 1
Assumptions1. The systolic blood pressure for males in the town is normally distributed.
. The mean systolic blood pressure is130.
3. The standard deviation of the systolic blood pressure is10.
4.105 males are randomly selected for the study.
5. We need to find the number of males expected to have a systolic blood pressure less than154.
STEP 2
First, we need to calculate the z-score for a systolic blood pressure of154. The z-score is a measure of how many standard deviations an element is from the mean. It can be calculated using the formulawhere X is the value we are interested in, μ is the mean, and σ is the standard deviation.
STEP 3
Now, plug in the given values for X, μ, and σ to calculate the z-score.
STEP 4
Calculate the z-score.
STEP 5
The z-score tells us that a systolic blood pressure of154 is2.4 standard deviations above the mean. Now, we need to find the proportion of males expected to have a systolic blood pressure less than154. This is equivalent to finding the cumulative probability for a z-score of2.4. This can be found using a standard normal distribution table or a calculator with a normal distribution function.
The cumulative probability for a z-score of2.4 is approximately0.9918. This means that about99.18% of males are expected to have a systolic blood pressure less than154.
STEP 6
Finally, we need to find the number of males expected to have a systolic blood pressure less than154. We can do this by multiplying the cumulative probability by the total number of males in the study.
STEP 7
Plug in the values for the cumulative probability and the total number of males to calculate the number of males.
STEP 8
Calculate the number of males expected to have a systolic blood pressure less than154.
So, we would expect about104 males to have a systolic blood pressure less than154.
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