In a population of normally distributed aptitude scores of 1000 academy students with mean 70 and Standard deviation 10, how many score above 95?

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 that proportion by 1000. (Round to whole students.)

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To find out how many students scored above 95 in a population of normally distributed aptitude scores, we need to calculate the area under the normal curve that is above the value of 95.

Here are the steps to calculate this:

Step 1: Standardize the score
We start by standardizing the score of 95. Standardizing a score means converting it into a z-score, which tells us how many standard deviations away from the mean the score is. The formula for calculating the z-score is:
z = (x - mean) / standard deviation

In this case, the score we want to standardize (x) is 95, the mean is 70, and the standard deviation is 10. Plugging these values into the formula, we get:
z = (95 - 70) / 10
z = 25 / 10
z = 2.5

So the standardized score for 95 is 2.5.

Step 2: Find the area under the curve
Now we need to find the area under the normal curve that is above the z-score of 2.5. We can use a standard normal distribution table or a statistical calculator for this.

Looking up the z-score of 2.5 in a standard normal distribution table, we find that the area to the left of 2.5 is approximately 0.9938. Since we want the area above 2.5, we subtract this value from 1:
Area above 2.5 = 1 - 0.9938 = 0.0062

So the area under the normal curve above the z-score of 2.5 is approximately 0.0062.

Step 3: Calculate the number of students
Finally, to determine the number of students who scored above 95, we need to multiply the area above 2.5 by the total number of students in the population. In this case, the population size is 1000.

Number of students above 95 = Area above 2.5 * Population size
= 0.0062 * 1000
= 6.2

Therefore, the estimated number of academy students who scored above 95 is 6.2. Since the population cannot have fractional students, we can round this to the nearest whole number. Thus, approximately 6 students scored above 95.