Answer to Question #285195 in Statistics and Probability for Ailynarboiz

Question

The iq of 300 students in a certain school in Quezon province is approximately normally distributed with mean of 100 and standard deviation is 15??

Answer 1

Sample size (n) = 300

Mean = 100

Standard deviation = 15

The percentage of students have an IQ from 85 to 120 is:

$P(85<X<120)=P(\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<Z<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}})$

$P(85<X<120)=P(\frac{85-100}{\frac{15}{\sqrt{300}}}<Z<\frac{120-100}{\frac{15}{\sqrt{300}}})$

$P(85<X<120)=P(-17.32<Z<23.09)$

$(85<X<120)=P(Z<23.09)-(Z<-17.32)$

Find probability in respect to each Z score using standard distribution table.

$(85<X<120)=1.0-0.00=1.0\approx100\%$

This means approximately 100% students have an IQ from 85 to 120.