Respuesta :
Between 77 and 129
Here, we want to describe where the lowest 5% and the highest 5% of IQ scores lie
What we need here is the appropriate z-score that corresponds to both the lowest 5% and the highest 5%
For the lowest 5%, we have a z-score of -1.645 while for the highest 5% (95% - 100%), we have a z-score of 1.645
Mathematically, the formula for calculating the z-score for a normal distribution is as follows;
[tex]\text{Z}_{score\text{ }}=\text{ }\frac{(x\text{ - }\mu)}{\sigma}[/tex]Where σ is the standard deviation = 13 and μ = 103 which is the mean. X refer to the raw IQ scores which we are trying to calculate
Thus;
for z = -1.645
[tex]\begin{gathered} -1.645\text{ = }\frac{(x-103)}{13} \\ \\ 13(-1.645)\text{ = x-103} \\ \\ -21.385\text{ = x -103} \\ x\text{ = 103 - 21.385} \\ \\ x\text{ = 81.615 } \\ \\ \text{approx. 82} \end{gathered}[/tex]For z = 1.645
[tex]\begin{gathered} 1.645\text{ = }\frac{(x-103)}{13} \\ \\ x-103\text{ = 13(1.645)} \\ \\ x-103\text{ = 21.385} \\ \\ x\text{ = 21.385 + 103} \\ x\text{ = 124.385} \\ \\ \text{approx 124} \end{gathered}[/tex]So we have the range of between 82 and 124
We now proceed to the options to check the best fit
The best fit here is between 77 and 129
