Question

Autism South Africa knows the true population proportion of children with autism is special need school is 0.74. Assume a sample size of 100 children with autism is selected, what is the probability that the sample proportion is between 0.7 and 0.84?

Answer 1

This is a normal distribution with $\hat{p}=0.74, \;\sigma=\sqrt{\frac{0.74(1-0.74)}{100}}=0.0439.$

$P(0.7<X<0.84)=P(\frac{0.7-0.74}{0.0439}<Z<\frac{0.84-0.74}{0.0439})=P(-0.91<Z<2.28)=0.8073.$