Question

For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure.

Answer 1

Answer:

Lower limit: 113.28

Upper limit: 126.72

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 120, \sigma = 8$

Middle 60%

So it goes from X when Z has a pvalue of 0.5 - 0.6/2 = 0.2 to X when Z has a pvalue of 0.5 + 0.6/2 = 0.8

Lower limit

X when Z has a pvalue of 0.20. So X when $Z = -0.84$

$Z = \frac{X - \mu}{\sigma}$

$-0.84 = \frac{X - 120}{8}$

$X - 120 = -0.84*8$

$X = 113.28$

Upper limit

X when Z has a pvalue of 0.80. So X when $Z = 0.84$

$Z = \frac{X - \mu}{\sigma}$

$0.84 = \frac{X - 120}{8}$

$X - 120 = 0.84*8$

$X = 126.72$