Question

Thirty percent 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

Answer: 0.9088  

Step-by-step explanation:

Given : $\mu=0.30$

$\sigma=0.045$  

Let x be a random available that represents the proportion of students that reads below grade level .

Using $z=\dfrac{x-\mu}{\sigma$ , for x= 0.36 , we have

$z=\dfrac{0.36-0.30}{0.045}=1.33333$

Using standard normal z-value table,

P-value $= P(<z<1.33333)=$

$P(z<1.33)=0.9087882\approx0.9088$ [Rounded yo the nearest 4 decimal places.]

Hence, the probability that a second sample would be selected with a proportion less than 0.36 = 0.9088