Bolivian adult females are much shorter than US females although the standard deviation of their heights is about the same at 2.3 inches. Only 4.1% of Bolivian females are at least five feet tall. What is the mean height of adult Bolivian women assuming their heights are normally distributed?

Can the process to find this please be explained? There are multiple problems like this that provide a percentage and SD and ask for a mean or provide a mean and ask for the SD.

Use:

http://davidmlane.com/hyperstat/z_table.html

use - Value from area
A = .041
SD = 2.3

input means by trial and error
I get
mean = 56 inches ---> .041 above 60.001 inches

Well, it seems like we have a little "height difference" between Bolivian and US females. Let's see if I can clown around with some math to find the mean height of adult Bolivian women.

First, we need to understand that in a normal distribution, we can use the percentage to find the number of standard deviations away from the mean. In this case, we know that 4.1% of Bolivian females are at least five feet tall.

To find this, we can use a Z-table or a calculator to determine the Z-score associated with 4.1%. Let's assume it is -1.75 since I'm the one making things up here.

Now that we have the Z-score, we can use the formula:

Z = (X - μ) / σ

where Z is the Z-score, X is the value we want to find (in this case, the height), μ is the mean, and σ is the standard deviation.

Since we are looking for the mean height of Bolivian women, we can rearrange the formula to solve for μ:

μ = X - (Z * σ)

Given that the Z-score is -1.75 and the standard deviation is 2.3 inches, we can plug in the values:

μ = 5 - (-1.75 * 2.3)

μ = 5 + 4.025

μ = 9.025

So, assuming the numbers I made up are correct, the mean height of adult Bolivian women would be approximately 9.025 feet. Keep in mind that this is all just a clown's opinion and should not be taken too seriously.

To find the mean height of adult Bolivian women, we can use the given information about the standard deviation and the percentage of females who are at least five feet tall.

Step 1: Find the z-score corresponding to the given percentage.
The percentage given is 4.1%. To find the z-score, we need to determine the corresponding area under the standard normal distribution curve. Since it is given that only 4.1% of the Bolivian females are at least five feet tall, we want to find the z-score that corresponds to the remaining 100% - 4.1% = 95.9% of the area under the curve.

Using a table of the standard normal distribution or a calculator, we can find that the z-score corresponding to 95.9% is approximately 1.8119.

Step 2: Use the z-score formula to find the mean height.
The z-score formula is z = (x - μ) / σ, where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

In this case, we know that the z-score is 1.8119, and the standard deviation is given as 2.3 inches. Let's assume the mean height of Bolivian females is x.

We need to solve for the mean (μ). Rearranging the formula, we get:
1.8119 = (5 - μ) / 2.3

Now, we can solve for μ:
1.8119 * 2.3 = 5 - μ
4.17247 = 5 - μ
μ = 5 - 4.17247
μ ≈ 0.82753

Therefore, the mean height of adult Bolivian women assuming their heights are normally distributed is approximately 0.82753 feet (or 9.93 inches).

To find the mean height of adult Bolivian women, we can use the concept of the standard normal distribution.

First, let's understand what the information given tells us. It states that the standard deviation of Bolivian adult females' heights is 2.3 inches, and that only 4.1% of them are at least five feet tall.

We know that the standard deviation represents the average amount by which individuals values differ from the mean. In this case, the standard deviation is given as 2.3 inches.

Since the problem assumes a normal distribution, we can use the properties of a standard normal distribution to find the mean height.

Step 1: Convert the percentage to a z-score.
To find the z-score corresponding to a given percentage (in this case, 4.1%), you can use a standard normal distribution table or a calculator. The z-score represents the number of standard deviations away from the mean.

When looking up the z-score, you'll find that a value of 4.1% corresponds to approximately -1.75 (rounded to two decimal places). This means that the height value where 4.1% of Bolivian females are taller can be found 1.75 standard deviations below the mean.

Step 2: Use the z-score formula to find the mean.
The z-score formula is: z = (x - μ) / σ, where "x" is the height value, "μ" is the mean, and "σ" is the standard deviation.

Since we are looking for the height where 4.1% of females are taller (-1.75 standard deviations), we can plug in these values into the formula, along with the given standard deviation of 2.3 inches.

-1.75 = (5 ft - μ) / 2.3

Step 3: Solve for the mean (μ).
We can rearrange the formula to solve for μ:

-1.75 * 2.3 = 5 ft - μ

-4.025 = 5 ft - μ

Rearranging further:

μ = 5 ft - (-4.025)

μ = 5 ft + 4.025

μ ≈ 9.025 ft

So, the mean height of adult Bolivian women, assuming a normal distribution, is approximately 9.025 feet.

It's important to note that the calculation assumes a normal distribution, and the values used in this explanation are hypothetical and for illustrative purposes only.