A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score higher than 71 on this exam?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

To find the probability of getting a score higher than 71 on this exam, we can use the standard normal distribution table or the Z-score formula.

Step 1: Calculate the Z-score.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
X = The score we want to find the probability for (71 in this case)
μ = The mean of the distribution (73 in this case)
σ = The standard deviation of the distribution (8 in this case)

Z = (71 - 73) / 8
Z = -2 / 8
Z = -0.25

Step 2: Find the probability using the standard normal distribution table.
Using the standard normal distribution table or a calculator, we can find the probability associated with the Z-score of -0.25. Looking up this value on the table, we find that the probability is approximately 0.4013.

So, the probability of getting a score higher than 71 on this exam is approximately 0.4013 or 40.13%.

To find the probability of getting a score higher than 71 on this exam, we need to use the properties of the normal distribution.

Step 1: Standardize the score
To standardize the score, we need to calculate the z-score using the formula:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.
In this case, x = 71, μ = 73, and σ = 8.
Plugging in the values, we get:
z = (71 - 73) / 8
z = -0.25

Step 2: Find the probability
Now, we need to find the probability of getting a score higher than 71. We can use a standard normal distribution table or a calculator to find this probability.

Using the standard normal distribution table:
Look up the z-score -0.25 in the table, and find the corresponding cumulative probability. Since we are looking for the probability of getting a score higher than 71, we need to find the area to the right of the z-score. Using the table, we find that the cumulative probability for a z-score of -0.25 is approximately 0.5987.
However, since we want the probability of getting a score higher than 71, we subtract this cumulative probability from 1:
P(score > 71) = 1 - 0.5987
P(score > 71) ≈ 0.4013

Using a calculator:
Using a calculator with the ability to compute normal distribution probabilities, input the z-score -0.25 and specify that you want the probability of getting a score higher than 71. The output should give you the probability, which is approximately 0.4013.

Therefore, the probability of getting a score higher than 71 on this exam is approximately 0.4013, or 40.13%.