The heights of 500 boys are measured and found to be normally distrubuted with a mean of 66 inches and a standard deviation of 2 inches.About how many boys are taller than 68 inches?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score. Multiply by 500.
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To find out how many boys are taller than 68 inches, we need to use the concept of the standard normal distribution and the z-score.
The z-score represents the number of standard deviations an individual value is from the mean. We can calculate the z-score using the formula:
z = (x - μ) / σ
Where:
x = individual value (in this case, 68 inches)
μ = mean (66 inches)
σ = standard deviation (2 inches)
Substituting the values into the formula:
z = (68 - 66) / 2
z = 2 / 2
z = 1
Now, we need to find the probability of an individual being taller than 68 inches. We can do this by looking up the z-score on a standard normal distribution table.
For a z-score of 1, the corresponding proportion or probability is approximately 0.8413. This means that approximately 84.13% of the values are below 68 inches.
To find out how many boys are taller than 68 inches, we subtract the proportion from 1 (since we want those taller than 68 inches). So:
1 - 0.8413 = 0.1587
This means that about 15.87% of the boys are taller than 68 inches.
To determine the number of boys, we multiply this proportion by the total number of boys (500):
0.1587 * 500 ≈ 79.35
Therefore, approximately 79 boys are taller than 68 inches.