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

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
, for x= 0.36 , we have

`z=(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