Questions: Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=(x-μ)/σ ? μ=0 σ=1 The original pulse rates are measured with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. A. The z scores are measured with units of "beats." B. The z scores are measured with units of "minutes per beat." C. The z scores are measured with units of "beats per minute." D. The z scores are numbers without units of measurement.

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=(x-μ)/σ ? μ=0 σ=1 The original pulse rates are measured with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. A. The z scores are measured with units of "beats." B. The z scores are measured with units of "minutes per beat." C. The z scores are measured with units of "beats per minute." D. The z scores are numbers without units of measurement.
Transcript text: Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to $z$ scores using $z=\frac{(x-\mu)}{\sigma}$ ? \[ \begin{array}{l} \mu=0 \\ \sigma=1 \end{array} \] The original pulse rates are measured with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. A. The $z$ scores are measured with units of "beats." B. The $z$ scores are measured with units of "minutes per beat." C. The $z$ scores are measured with units of "beats per minute." D. The $z$ scores are numbers without units of measurement.
failed

Solution

failed
failed

Solution Steps

Step 1: Mean and Standard Deviation of Z-scores

When converting pulse rates to z z -scores using the formula

z=(x−μ)σ z = \frac{(x - \mu)}{\sigma}

the mean (μ \mu ) of the z z -scores becomes 0 0 and the standard deviation (σ \sigma ) becomes 1 1 . Therefore, we have:

Mean of z-scores=0 \text{Mean of } z\text{-scores} = 0 Standard deviation of z-scores=1 \text{Standard deviation of } z\text{-scores} = 1

Step 2: Units of Z-scores

The z z -scores are dimensionless quantities, meaning they do not have any units of measurement. This is because z z -scores represent the number of standard deviations a data point is from the mean, which cancels out the units. Thus, we conclude that:

The z scores are numbers without units of measurement. \text{The } z \text{ scores are numbers without units of measurement.}

Final Answer

The mean of the z z -scores is 0 0 , the standard deviation of the z z -scores is 1 1 , and the z z -scores are numbers without units of measurement.

Mean=0,Standard Deviation=1,Units=none\boxed{\text{Mean} = 0, \text{Standard Deviation} = 1, \text{Units} = \text{none}}

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
If z is a standard normal variable, find the probability P(-0.73<z<2.27). Round to four decimal places. A. 0.4884 B. 1.5400 C. 0.7557 D. 0.2211
failedAnswered
Which of the following genetic diseases affect males and females equally? a. cystic fibrosis b. hemophilia c. color-blindness d. muscular dystrophy
failedAnswered
4.8 t-3=3.8 t-3 The solution set is □
failedAnswered
Neoclassical ballet choreographers focus on the structure of movement in space. True False
failedAnswered
What can be said regarding Smith Son's accounts receivable turnover for Year 2? O It improved from Year 1 to Year 2. O It collected its accounts receivables less effectively in Year 2 as compared to Year 1. O fewer customers purchased items on account during Year 2 as compared to Year 1. O Customers paid their account balances more quickly during Year 2 as compared to Year 1.