assume that blood pressure readings are normally distributed with a mean of 111 and standard deviation of 7. A researcher wishes to select people for a study but wants to exclude the top and bottom 10 percent. What would be the upper and lower readings to qualify people to participate in the study?
the central 80% of the Z table lies within µ ± 1.282σ
So, plug in your numbers
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To find the upper and lower readings to qualify people for the study, we need to determine the cutoff values at which we exclude the top and bottom 10% of blood pressure readings.
Step 1: Determine the z-score for the cutoff values
The z-score measures how many standard deviations a value is from the mean. To find the z-score for the cutoff values, we use the standard normal distribution table or calculate it using the formula:
z = (x - μ) / σ
For the upper cutoff value, we want to find the z-score that corresponds to excluding the top 10% of readings. Using the standard normal distribution table, we look for the z-score that corresponds to a cumulative probability of 0.90. The closest value is approximately 1.28.
For the lower cutoff value, we want to find the z-score that corresponds to excluding the bottom 10% of readings. Using the standard normal distribution table, we look for the z-score that corresponds to a cumulative probability of 0.10. The closest value is approximately -1.28.
Step 2: Calculate the corresponding blood pressure values
Once we have the z-scores, we can calculate the corresponding blood pressure values using the formula:
x = μ + (z * σ)
For the upper cutoff value:
x_upper = 111 + (1.28 * 7)
= 119.96 (approximately 120)
For the lower cutoff value:
x_lower = 111 + (-1.28 * 7)
= 102.96 (approximately 103)
Therefore, to qualify people to participate in the study, the upper reading would be approximately 120 and the lower reading would be approximately 103.