Question

4. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. In a
random sample of 900, approximately how many people will have IQs between 85 and 120?
​

Answer 1

675 people will have score between 85 and 120

Step-by-step explanation:

Given

Mean = 100

SD = 15

If we have to find percentage of score between two values we have to find the z-score for both values and then area under the curve for both values

z-score is given by:

for a value x:

$z-score = \frac{x-mean}{SD}$

So,

For 85:

$z-score = z_1 = \frac{85-mean}{SD}\\ = \frac{85-100}{15}\\=\frac{-15}{15}\\=-1$

$z-score = z_2 = \frac{120-mean}{SD}\\ = \frac{120-100}{15}\\=\frac{20}{15}\\=1.3333$

Now we have to find the area under the curve for both values of z-score. z-score tables are used for this purpose.

So,

For z1 : 0.1587

For z2: 0.9082

The area between z11 and z2:

$z_2-z_1 = 0.9082-0.1587=0.7495$

So the probability of score between 85 and 120 is 0.7495

As the sample is of 900 people, the people with scores between 85 and 120 will be:

900*0.7495 = 674.55 people

Rounding off to nearest whole number

675 people will have score between 85 and 120

Keywords: Probability, SD

Learn more about probability at:

• brainly.com/question/10978510
• brainly.com/question/11007026

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