Math / Algebra

QuestionCheck here for instructional material to complete this problem. Evaluate $z=\frac{x-\mu}{\sigma}$ if $x=177, \mu=171$ , and $\sigma=6$ $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We're given a formula for $z$ and values for $x$ , $\mu$ , and $\sigma$ , and we need to plug them in and calculate the result! Watch out! Make sure to follow the order of operations correctly, and don't forget to round to two decimal places at the end.

STEP 2

1. Plug in the values
2. Calculate the numerator
3. Calculate the fraction

STEP 3

We are given $x = \textbf{177}$ , $\mu = \textbf{171}$ , and $\sigma = \textbf{6}$ .
These are our key ingredients for the formula!

STEP 4

Now, let's carefully plug these values into our formula for $z$ : $z = \frac{x - \mu}{\sigma} = \frac{\textbf{177} - \textbf{171}}{\textbf{6}}$ See how we replaced $x$ , $\mu$ , and $\sigma$ with their given values?

STEP 5

Let's tackle the numerator first: $\textbf{177} - \textbf{171} = \textbf{6}$ .
So, our formula now looks like this: $z = \frac{\textbf{6}}{\textbf{6}}$

STEP 6

Now, we divide the numerator by the denominator: $\textbf{6}$ divided by $\textbf{6}$ equals $\textbf{1}$ .
So, we have: $z = \textbf{1}$

STEP 7

Our final answer is $z = \textbf{1.00}$ .
Remember, the problem asked us to round to two decimal places!

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QuestionCheck here for instructional material to complete this problem. Evaluate $z=\frac{x-\mu}{\sigma}$ if $x=177, \mu=171$ , and $\sigma=6$ $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We're given a formula for $z$ and values for $x$ , $\mu$ , and $\sigma$ , and we need to plug them in and calculate the result! Watch out! Make sure to follow the order of operations correctly, and don't forget to round to two decimal places at the end.

STEP 2

1. Plug in the values
2. Calculate the numerator
3. Calculate the fraction

STEP 3

We are given $x = \textbf{177}$ , $\mu = \textbf{171}$ , and $\sigma = \textbf{6}$ .
These are our key ingredients for the formula!

STEP 4

Now, let's carefully plug these values into our formula for $z$ : $z = \frac{x - \mu}{\sigma} = \frac{\textbf{177} - \textbf{171}}{\textbf{6}}$ See how we replaced $x$ , $\mu$ , and $\sigma$ with their given values?

STEP 5

Let's tackle the numerator first: $\textbf{177} - \textbf{171} = \textbf{6}$ .
So, our formula now looks like this: $z = \frac{\textbf{6}}{\textbf{6}}$

STEP 6

Now, we divide the numerator by the denominator: $\textbf{6}$ divided by $\textbf{6}$ equals $\textbf{1}$ .
So, we have: $z = \textbf{1}$

STEP 7

Our final answer is $z = \textbf{1.00}$ .
Remember, the problem asked us to round to two decimal places!

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QuestionCheck here for instructional material to complete this problem. Evaluate z=x−μσz=\frac{x-\mu}{\sigma}z=σx−μ​ if x=177,μ=171x=177, \mu=171x=177,μ=171, and σ=6\sigma=6σ=6 z=z=z= □\square□ (Type an integer or decimal rounded to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We're given a formula for zzz and values for xxx, μ\muμ, and σ\sigmaσ, and we need to plug them in and calculate the result! Watch out! Make sure to follow the order of operations correctly, and don't forget to round to two decimal places at the end.

STEP 2

1. Plug in the values2. Calculate the numerator3. Calculate the fraction

STEP 3

We are given x=177x = \textbf{177}x=177, μ=171\mu = \textbf{171}μ=171, and σ=6\sigma = \textbf{6}σ=6.These are our **key ingredients** for the formula!

STEP 4

Now, let's carefully **plug these values** into our formula for zzz: z=x−μσ=177−1716z = \frac{x - \mu}{\sigma} = \frac{\textbf{177} - \textbf{171}}{\textbf{6}}z=σx−μ​=6177−171​ See how we replaced xxx, μ\muμ, and σ\sigmaσ with their given values?

STEP 5

Let's **tackle the numerator** first: 177−171=6\textbf{177} - \textbf{171} = \textbf{6}177−171=6.So, our formula now looks like this: z=66z = \frac{\textbf{6}}{\textbf{6}}z=66​

STEP 6

Now, we **divide the numerator by the denominator**: 6\textbf{6}6 divided by 6\textbf{6}6 equals 1\textbf{1}1.So, we have: z=1z = \textbf{1}z=1

STEP 7

Our **final answer** is z=1.00z = \textbf{1.00}z=1.00.Remember, the problem asked us to round to two decimal places!

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Studdy solves anything!

Start learning now

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

QuestionCheck here for instructional material to complete this problem. Evaluate $z=\frac{x-\mu}{\sigma}$ if $x=177, \mu=171$ , and $\sigma=6$ $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

What is this asking? We're given a formula for $z$ and values for $x$ , $\mu$ , and $\sigma$ , and we need to plug them in and calculate the result! Watch out! Make sure to follow the order of operations correctly, and don't forget to round to two decimal places at the end.

1. Plug in the values
2. Calculate the numerator
3. Calculate the fraction

We are given $x = \textbf{177}$ , $\mu = \textbf{171}$ , and $\sigma = \textbf{6}$ .
These are our key ingredients for the formula!

Now, let's carefully plug these values into our formula for $z$ : $z = \frac{x - \mu}{\sigma} = \frac{\textbf{177} - \textbf{171}}{\textbf{6}}$ See how we replaced $x$ , $\mu$ , and $\sigma$ with their given values?

Let's tackle the numerator first: $\textbf{177} - \textbf{171} = \textbf{6}$ .
So, our formula now looks like this: $z = \frac{\textbf{6}}{\textbf{6}}$

Now, we divide the numerator by the denominator: $\textbf{6}$ divided by $\textbf{6}$ equals $\textbf{1}$ .
So, we have: $z = \textbf{1}$

Our final answer is $z = \textbf{1.00}$ .
Remember, the problem asked us to round to two decimal places!