Answer :
Final answer:
Approximately 29.50% of students have an IQ score less than 92.
Explanation:
To find the percentage of students with an IQ score less than 92, we can use the normal distribution and the z-score formula.
The z-score measures how many standard deviations a particular value is from the mean.
First, we need to convert the IQ score of 92 to a z-score.
The formula is: z = (x - µ) / σ { where x is the given value, µ is the mean, and σ is the standard deviation }.
In this case, x = 92, µ = 100, and σ = 15.
Plugging in the values, we get:
z = (92 - 100) / 15 = -0.5333
Using a z-table or calculator, we can find the area under the curve to the left of z = -0.5333.
This gives us the percentage of students with an IQ score less than 92.
According to the z-table, the area to the left of z = -0.5333 is approximately 0.2950.
Therefore, approximately 29.50% of students have an IQ score less than 92.
