QuestionQuestion 4
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a -score of 0.3571 (to 4 decimal places)
Studdy Solution
STEP 1
What is this asking?
We need to find a tall dude's height using some fancy math stats!
Watch out!
Don't mix up the formula!
Remember, we're going from z-score to actual height, not the other way around.
STEP 2
1. Recall the z-score formula
2. Rearrange the formula
3. Plug in the values
4. Calculate the height
STEP 3
Alright, let's kick things off by remembering what a z-score actually is!
It's like a measurement of how far away a value is from the mean, but in terms of standard deviations.
Cool, right?
STEP 4
The formula for a z-score looks like this:
Where **z** is our z-score, **x** is the value we're looking for (in this case, the height), **μ** (that's the Greek letter mu) is the mean, and **σ** (sigma) is the standard deviation.
But wait, we actually want to solve for **x**, not **z**!
STEP 5
Time to flip this formula on its head!
We want to isolate **x**, so let's do some algebra magic.
First, let's multiply both sides by **σ**:
STEP 6
Now, let's add **μ** to both sides:
Boom! We've got our formula to find the height.
This is telling us that the height is equal to the z-score times the standard deviation, plus the mean.
It's like we're starting at the average height and then moving up or down based on the z-score!
STEP 7
Let's gather all our ingredients: - z-score (**z**) = **0.3571** - Mean height (**μ**) = **69.0** inches - Standard deviation (**σ**) = **2.8** inches
STEP 8
Now, let's substitute these values into our rearranged formula:
STEP 9
Time to crunch those numbers!
Let's start with the part in parentheses:
STEP 10
Now, let's add this to our mean height:
STEP 11
The question asks for 4 decimal places, so let's round our answer:
STEP 12
The height of a man with a z-score of 0.3571 is **70.0000** inches.
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