find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and and a standard deviation of 15
The shaded area under the curve is 0.10
119.2
100.5
108.1
80.8
PSYDAG it is to the right, can you help with this answer still?
To find the indicated IQ score, we need to convert the shaded area into a Z-score and then reverse the calculation to find the corresponding IQ score. The Z-score formula is given by:
Z = (X - μ) / σ
Where:
Z = Z-score
X = IQ score
μ = Mean IQ score
σ = Standard deviation of IQ scores
In this case, we are given that the shaded area under the curve is 0.10. Since the area represents the probability, we can find the Z-score corresponding to this area using a Z-table or a statistical calculator.
The Z-score that corresponds to an area of 0.10 is approximately -1.28. Using the Z-score formula and solving for X, we have:
-1.28 = (X - 100) / 15
Solving for X gives:
X = -1.28 * 15 + 100
X = 80.8
Therefore, the indicated IQ score is approximately 80.8.
To summarize:
- The indicated IQ score is 80.8.
To find the indicated IQ score, we need to use the Z-score formula and the standard Normal distribution table (also known as the Z-table).
The Z-score formula is:
Z = (X - μ) / σ
where:
X = the specific IQ score we're trying to find
μ = the mean IQ score (100 in this case)
σ = the standard deviation (15 in this case)
First, we need to find the corresponding Z-score for the shaded area of 0.10. Since the area is shaded to the left of the Z-score, we can look up the Z-score that corresponds to a cumulative probability of 0.10 in the Z-table.
By looking up the Z-table or using statistical software, we find that the Z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
Now, we can plug this Z-score into the Z-score formula and solve for X (the IQ score):
-1.28 = (X - 100) / 15
Multiply both sides of the equation by 15:
-1.28 * 15 = X - 100
-19.2 = X - 100
Now, let's solve for X:
X = -19.2 + 100
X = 80.8
So, the indicated IQ score is 80.8.
Therefore, the correct answer is 80.8.