The number of people that have an IQ between 71 and 118, to the nearest whole number is 1030.
A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
Z = (X-μ)/σ
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
Given the mean is 100, while the standard deviation is 15. Therefore, we can write,
P(71≤X≤118) = P(X≤118) - P(X≤71)
[tex]= P(Z\leq \dfrac{118-100}{15}) - P(Z\leq \dfrac{71-100}{15})\\\\= P(Z\leq 1.2) - P(Z\leq -1.933)\\\\= 0.8849 - 0.0268\\\\= 0.8581[/tex]
Thus, of the population of 1200, 85.81% of the people will have an IQ between 71 and 118. Therefore, the number of people who have the IQ between 71 and 118 are:
Number of people = 1200 × 0.8581 = 1029.72 ≈1030
Hence, the number of people that have an IQ between 71 and 118, to the nearest whole number is 1030.
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