Use the following information to answer questions (8) - (10). Suppose that the mean Systolic blood pressure for
adults age 50-54 is 125 mmHg with a standard deviation of 5 mmHg. It is known that Systolic blood pressure is not
Normally distributed. Suppose a sample of 25 adult Systolic blood pressure measurements is taken from the
population.
-What is the interpretation of the z score used to find the probability that the average Systolic blood pressure will be less than 122 mmHg? Assume technology is not available and so the values must first be converted to standard units. Round to the nearest hundredth.
A)z = -3.00 which is less than or equal to 3 standard deviations above the mean.
B)z = -3.00 which is less than or equal to 3 standard deviations below the mean.
C)z = 3.00 which is less than or equal to 3 standard deviations above the mean.
D)This probability cannot be determined because we do not know the distribution of the population.

Question

Quizplus · Accepted Answer

The z-score is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 122$, $\mu = 125$, $\sigma = 5$, $n = 25$), we get $z = \frac{122 - 125}{5/\sqrt{25}} = \frac{-3}{1} = -3.00$. This indicates that the sample mean is 3 standard deviations below the population mean.

Use the Following Information to Answer Questions (8) - (10)