A normal distribution has a mean of 36 and standard deviation of 4. What proportion of the
distribution consisted of scores between x=34 and x=38?
a, 0.6915
b, 2(0.3085)=0.6170
c, 0.1915
d, 2(0.1915)=0.3930
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.
To find the proportion of the distribution consisting of scores between x=34 and x=38, we can use the standard normal distribution.
First, we need to convert the given values to z-scores using the formula:
z = (x - μ) / σ
where z is the standard score, x is the value we want to convert, μ is the mean, and σ is the standard deviation.
For x = 34:
z = (34 - 36) / 4 = -0.5
For x = 38:
z = (38 - 36) / 4 = 0.5
Now, we need to calculate the proportion between these two z-scores.
Using a z-table or a calculator, we can find the corresponding area under the standard normal curve between -0.5 and 0.5, which is 0.3829.
However, since we want the proportion between x=34 and x=38 on both sides of the mean, we need to double this value:
2 * 0.3829 = 0.7658
So, the correct answer is not provided in the options.
To find the proportion of a normal distribution between two scores, we need to calculate the area under the normal curve between those two scores.
In this case, we want to find the proportion of scores between x = 34 and x = 38, given that the mean is 36 and the standard deviation is 4.
First, we need to convert these scores into z-scores, as the normal distribution is standardized with a mean of 0 and a standard deviation of 1. We use the formula:
z = (x - mean) / standard deviation
For x = 34:
z1 = (34 - 36) / 4
z1 = -0.5
For x = 38:
z2 = (38 - 36) / 4
z2 = 0.5
Next, we need to find the area under the curve between these two z-scores. We can use a standard normal distribution table or a calculator to find these values.
From the standard normal distribution table or calculator, the area to the left of z = 0.5 is 0.6915, and the area to the left of z = -0.5 is 0.3085.
To find the proportion between z1 and z2, we subtract the lower area from the higher area:
Proportion = 0.6915 - 0.3085
Proportion = 0.3830
Since we want the proportion between x = 34 and x = 38, and not just one tail of the distribution, we need to double this proportion:
Proportion = 2(0.3830)
Proportion = 0.7660
Therefore, the correct answer is not one of the options provided. The correct proportion is 0.7660, which is not listed.