Suppose that the test scores for a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100. If a student is selected at random what is the probability that
the student will score above 600?
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.
6.6%
To find the probability that a student will score above 600 on the test, we can use the normal distribution and the given mean and standard deviation.
First, we need to standardize the value of 600 using the formula:
Z = (X - μ) / σ
where Z is the standardized score, X is the score we want to find the probability for (600 in this case), μ is the mean (450), and σ is the standard deviation (100).
Z = (600 - 450) / 100
Z = 150 / 100
Z = 1.5
Next, we need to find the probability corresponding to the standardized score using a standard normal distribution table or a calculator. The probability of a standardized score of 1.5 or higher corresponds to the area under the curve to the right of 1.5.
Looking up the value in a standard normal distribution table or using a calculator, we find that the probability of a standardized score of 1.5 or higher is approximately 0.0668.
Therefore, the probability that a student will score above 600 on the test is approximately 0.0668 or 6.68%.
To calculate the probability that a student will score above 600 on the college entrance exam, we need to use the concept of the standard normal distribution.
First, we need to transform the given normal distribution into a standard normal distribution by applying the formula:
Z = (X - μ) / σ
Where:
Z = the standard score
X = the given score
μ = the mean of the distribution
σ = the standard deviation of the distribution
In this case, the given score (X) is 600, the mean (μ) is 450, and the standard deviation (σ) is 100. Applying the formula, we can calculate the standard score (Z):
Z = (600 - 450) / 100
Z = 150 / 100
Z = 1.5
Now that we have the standard score, we can find the probability using a standard normal distribution table or a calculator. The probability of scoring above 600 can be found by subtracting the cumulative probability from the mean to the z-score of 1.5 from 1 (since we want the area to the right of the z-score).
By consulting a standard normal distribution table or using a calculator, we can find that the cumulative probability of a z-score of 1.5 is approximately 0.9332. Subtracting this value from 1 gives us the probability of scoring above 600:
P(X > 600) = 1 - 0.9332
P(X > 600) ≈ 0.0668
Therefore, the probability that a student selected at random will score above 600 on the college entrance exam is approximately 0.0668, or 6.68%.