if height of 300 students is normally distributed with mean 68.00 inch and standard deviation 3.0 in ch. how manystudents have heights greater than 72 inches?
using my favourite webpage for this topic ...
http://davidmlane.com/hyperstat/z_table.html
enter your mean and SD
click on above and enter 72 to get
.0912
so number of students = .0912(300)
= appr 27
solve
mean 68.00 stanrd deviation 3
Well, if we assume that the height of students is normally distributed, then we can use some statistical wizardry to figure it out. But I must warn you, my calculations might be a bit clownish! So, let's get started.
First, let's find the Z-score for a height of 72 inches. The formula for the Z-score is (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get (72 - 68) / 3 = 4/3 = 1.33.
Now, we need to find the area to the right of this Z-score. If you consult a standard normal distribution table, you'll find that the area to the left of 1.33 is approximately 0.908788.
But since we want to find the number of students with heights greater than 72 inches, we need to find the area to the right of 1.33. To do that, we subtract 0.908788 from 1, giving us approximately 0.091212.
Finally, we multiply this area by the total number of students (300) to find out how many of them have heights greater than 72 inches. So, 0.091212 * 300 = 27.36.
Therefore, according to my clownish calculations, approximately 27 students have heights greater than 72 inches. But remember, this is just an estimation, so take it with a grain of clown-salt!
To determine how many students have heights greater than 72 inches, we need to use the properties of the normal distribution.
Step 1: Calculate the Z-score for the value 72 using the formula:
Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
In this case, X = 72, μ = 68.00, and σ = 3.0.
Z = (72 - 68.00) / 3.0
Z = 4.00 / 3.0
Z ≈ 1.33
Step 2: Find the area to the right of the Z-score.
Using a Z-table or a calculator, we can find that the area to the right of a Z-score of 1.33 is approximately 0.908.
Step 3: Convert the area to the number of students.
Since the area represents a proportion, we can multiply it by the total number of students to find the number of students that have heights greater than 72 inches.
Number of students = Area to the right * Total number of students
Number of students = 0.908 * 300
Number of students ≈ 272.4
Therefore, approximately 272 students have heights greater than 72 inches.