The most common intelligence quotient (IQ) scale is normally distributed with mean 100 and standard deviation 15. What score would put a child 3 standard deviations above the mean
100 * 3(15) = 145
To find the score that would put a child 3 standard deviations above the mean, we need to calculate the value of 3 standard deviations and add it to the mean.
Given that the mean (μ) is 100 and the standard deviation (σ) is 15, we can use the formula:
x = μ + (z * σ)
where x is the score we are looking for, μ is the mean, z is the number of standard deviations, and σ is the standard deviation.
In this case, z is 3 since we want to find a score that is 3 standard deviations above the mean. Plugging in the values, we have:
x = 100 + (3 * 15)
x = 100 + 45
x = 145
Therefore, a score of 145 would put a child 3 standard deviations above the mean on the IQ scale.