Math / Data & Statistics

QuestionFind a $z$ -score for a data value of 7 if the mean of a set of data is 58 and the standard deviation is 16.9.
Round your answer to at least two decimal places. $\square$

Studdy Solution

STEP 1

1. The mean ( $\mu$ ) of the data set is 58.
2. The standard deviation ( $\sigma$ ) of the data set is 16.9.
3. The data value ( $X$ ) for which we need to find the $z$ -score is 7.
4. The formula for the $z$ -score is given by $z = \frac{X - \mu}{\sigma}$ .

STEP 2

1. Identify the values needed for the $z$ -score formula.
2. Substitute the values into the $z$ -score formula.
3. Calculate the $z$ -score and round to at least two decimal places.

STEP 3

Identify the values needed for the $z$ -score formula:
- Data value ( $X$ ): 7 - Mean ( $\mu$ ): 58 - Standard deviation ( $\sigma$ ): 16.9

STEP 4

Substitute the values into the $z$ -score formula:
$z = \frac{7 - 58}{16.9}$

STEP 5

Calculate the $z$ -score:
$z = \frac{-51}{16.9}$
$z \approx -3.02$
Round the $z$ -score to at least two decimal places:
$z \approx -3.02$
The $z$ -score is:
$\boxed{-3.02}$

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QuestionFind a $z$ -score for a data value of 7 if the mean of a set of data is 58 and the standard deviation is 16.9.
Round your answer to at least two decimal places. $\square$

Studdy Solution

STEP 1

1. The mean ( $\mu$ ) of the data set is 58.
2. The standard deviation ( $\sigma$ ) of the data set is 16.9.
3. The data value ( $X$ ) for which we need to find the $z$ -score is 7.
4. The formula for the $z$ -score is given by $z = \frac{X - \mu}{\sigma}$ .

STEP 2

1. Identify the values needed for the $z$ -score formula.
2. Substitute the values into the $z$ -score formula.
3. Calculate the $z$ -score and round to at least two decimal places.

STEP 3

Identify the values needed for the $z$ -score formula:
- Data value ( $X$ ): 7 - Mean ( $\mu$ ): 58 - Standard deviation ( $\sigma$ ): 16.9

STEP 4

Substitute the values into the $z$ -score formula:
$z = \frac{7 - 58}{16.9}$

STEP 5

Calculate the $z$ -score:
$z = \frac{-51}{16.9}$
$z \approx -3.02$
Round the $z$ -score to at least two decimal places:
$z \approx -3.02$
The $z$ -score is:
$\boxed{-3.02}$

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QuestionFind a zzz-score for a data value of 7 if the mean of a set of data is 58 and the standard deviation is 16.9.Round your answer to at least two decimal places. □\square□

Studdy Solution

STEP 1

1. The mean (μ\muμ) of the data set is 58.2. The standard deviation (σ\sigmaσ) of the data set is 16.9.3. The data value (XXX) for which we need to find the zzz-score is 7.4. The formula for the zzz-score is given by z=X−μσ z = \frac{X - \mu}{\sigma} z=σX−μ​.

STEP 2

1. Identify the values needed for the zzz-score formula.2. Substitute the values into the zzz-score formula.3. Calculate the zzz-score and round to at least two decimal places.

STEP 3

Identify the values needed for the zzz-score formula:- Data value (XXX): 7 - Mean (μ\muμ): 58 - Standard deviation (σ\sigmaσ): 16.9

STEP 4

Substitute the values into the zzz-score formula:z=7−5816.9 z = \frac{7 - 58}{16.9} z=16.97−58​

STEP 5

Calculate the zzz-score:z=−5116.9 z = \frac{-51}{16.9} z=16.9−51​z≈−3.02 z \approx -3.02 z≈−3.02Round the zzz-score to at least two decimal places:z≈−3.02 z \approx -3.02 z≈−3.02 The zzz-score is:−3.02 \boxed{-3.02} −3.02​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind a $z$ -score for a data value of 7 if the mean of a set of data is 58 and the standard deviation is 16.9.
Round your answer to at least two decimal places. $\square$

1. The mean ( $\mu$ ) of the data set is 58.
2. The standard deviation ( $\sigma$ ) of the data set is 16.9.
3. The data value ( $X$ ) for which we need to find the $z$ -score is 7.
4. The formula for the $z$ -score is given by $z = \frac{X - \mu}{\sigma}$ .

1. Identify the values needed for the $z$ -score formula.
2. Substitute the values into the $z$ -score formula.
3. Calculate the $z$ -score and round to at least two decimal places.

Identify the values needed for the $z$ -score formula:
- Data value ( $X$ ): 7 - Mean ( $\mu$ ): 58 - Standard deviation ( $\sigma$ ): 16.9

Substitute the values into the $z$ -score formula:
$z = \frac{7 - 58}{16.9}$

Calculate the $z$ -score:
$z = \frac{-51}{16.9}$
$z \approx -3.02$
Round the $z$ -score to at least two decimal places:
$z \approx -3.02$
The $z$ -score is:
$\boxed{-3.02}$