The SAT scores of a certain population of students are approximately normally distributed with a mean and standard deviation of 1000 and 200 points, respectively. The probability that a student selected at random from the population has an SAT score between 800 and 1200 approximately

Perfect data, one standard of devation below and above.

so appr 68% or prob of .68

confirmed by David's webpage
http://davidmlane.com/hyperstat/z_table.html

fill in the data to see and get .6827

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To find the probability that a student selected at random from the population has an SAT score between 800 and 1200, we need to standardize the scores using the z-score formula and then use the z-table to find the corresponding probabilities.

Step 1: Calculate the z-score for the lower bound:
z1 = (800 - 1000) / 200 = -1

Step 2: Calculate the z-score for the upper bound:
z2 = (1200 - 1000) / 200 = 1

Step 3: Use the z-table to find the probability corresponding to the z-scores.
From the z-table, the corresponding area/probability for z1 = -1 is 0.1587, and the corresponding area/probability for z2 = 1 is 0.8413.

Step 4: Calculate the probability between the two z-scores.
P(800 < x < 1200) = P(z1 < z < z2)
= P(z < z2) - P(z < z1)
= 0.8413 - 0.1587
= 0.6826

Therefore, the probability that a student selected at random from the population has an SAT score between 800 and 1200 is approximately 0.6826 or 68.26%.

To find the probability that a student selected at random from the population has an SAT score between 800 and 1200, we need to calculate the z-scores for these two scores and then find the area under the normal distribution curve between these z-scores.

First, we calculate the z-score for an SAT score of 800 using the formula:

z = (x - μ) / σ

Where:
x = SAT score (800)
μ = mean (1000)
σ = standard deviation (200)

z1 = (800 - 1000) / 200 = -1

Next, we calculate the z-score for an SAT score of 1200 using the same formula:

z2 = (1200 - 1000) / 200 = 1

Now that we have the z-scores, we can use a z-table or calculator to find the area under the normal distribution curve between these two z-scores.

Using a z-table, we can find that the area to the left of z = -1 is approximately 0.1587 and the area to the left of z = 1 is approximately 0.8413.

To get the area between these two z-scores, we subtract the smaller area from the larger area:

Area between z = -1 and z = 1 = 0.8413 - 0.1587 = 0.6826

Therefore, the probability that a student selected at random from the population has an SAT score between 800 and 1200 is approximately 0.6826 or 68.26%.