A normal distribution has µ = 80 and standard deviation = 10. What is the probability of randomly selecting a score greater than 75 from this distribution?
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. Use value between score and mean + .50 (for the scores above the mean).
To find the probability of randomly selecting a score greater than 75 from a normal distribution with µ = 80 and standard deviation = 10, we need to calculate the Z-score first.
The Z-score formula is:
Z = (X - µ) / σ
Where:
Z is the Z-score
X is the value we want to find the probability for (in this case, 75)
µ is the mean of the distribution (µ = 80)
σ is the standard deviation of the distribution (σ = 10)
Substituting the given values into the formula:
Z = (75 - 80) / 10
Z = -0.5
Next, we need to find the probability of a Z-score greater than -0.5 using a Z-table or an online calculator. The Z-table provides the area under the normal distribution curve up to a given Z-score.
Looking up the Z-score of -0.5 in the Z-table, we find that the area to the left of -0.5 is 0.3085. Since we want the area to the right of -0.5 (greater than -0.5), we subtract this value from 1:
Probability = 1 - 0.3085
Probability = 0.6915
Therefore, the probability of randomly selecting a score greater than 75 from this normal distribution is 0.6915, or 69.15%.
To find the probability of randomly selecting a score greater than 75 from a normal distribution with mean µ = 80 and standard deviation σ = 10, you can use the z-score formula and then consult a standard normal distribution table (also known as a z-table). Here are the steps to calculate it:
Step 1: Calculate the z-score:
The z-score formula is given by:
z = (x - µ) / σ
where x is the given value (75 in this case), µ is the mean (80), and σ is the standard deviation (10).
Substituting the values, we get:
z = (75 - 80) / 10
z = -0.5
Step 2: Consult the z-table:
The z-table provides the area under the standard normal distribution curve (to the left of the given z-score). To find the probability of selecting a score greater than 75, we want to find the area to the right of the z-score of -0.5.
Consulting the z-table, we find that the area to the left of -0.5 is 0.3085. Since we want the area to the right, we subtract this value from 1:
Area to the right = 1 - 0.3085
Area to the right ≈ 0.6915
Step 3: Convert the area to a probability:
The area under the distribution curve represents the probability. Therefore, the probability of randomly selecting a score greater than 75 from this distribution is approximately 0.6915, or 69.15%.
So, the probability of randomly selecting a score greater than 75 from this normal distribution is approximately 0.6915 or 69.15%.