Question

10 multiple choice 10 points
a standard iq test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12. approximately how many of these students would have iqs above 140?
317
650
624
51,366

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 140\), \(\mu=104\), and \(\sigma = 16\).

$$z=\frac{140 - 104}{16}=\frac{36}{16}=2.25$$

Step2: Find the probability using the standard normal distribution table

Looking up the value of \(P(Z\leq2.25)\) in the standard - normal table, we get \(P(Z\leq2.25)=0.9878\).
Then \(P(Z > 2.25)=1 - P(Z\leq2.25)=1-0.9878 = 0.0122\)

Step3: Calculate the number of students

Multiply the probability by the total number of students \(n = 52000\).
The number of students \(N=52000\times0.0122 = 634.4\approx624\) (using the closest value among the options)

Answer:

624