Question

30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?

Answer 1

The sampling distribution will have a mean of 0.30 and a standard deviation of 0.045

The required probability would be given by,

$P(\bar{x}\leq 0.36)=P\left(z<\frac{0.36-0.30}{0.045} \right )$

$P(\bar{x}\leq 0.36)=P\left(z<1.33\right )$

$P(\bar{x}\leq 0.36)=0.9088$