Suppose you know that the distribution of sample proportions of fifth grade students in a large school district who read below g
rade level in samples of 100 students is normal with a mean of 0.30 and a standard deviation of 0.12. You select a sample of 100 fifth grade students from this district and find that the proportion who read below grade level in the sample is 0.54. This sample proportion lies 2.0 standard deviations above the mean of the sampling distribution. What is the probability that a second sample would be selected with a proportion greater than 0.54 ?
Based on the mean of the sample and the proportion who read below grade level, the probability that a second sample would have a proportion greater than 0.54 is 0.9772.
<h3>What is the probability of the second sample being greater than 0.54?</h3>
The probability that the second sample would be selected with a proportion greater than 0.54 can be found as:
P (x > 0.54) = P ( z > (0.54 - 0.30) / 0.12))
Solving gives:
P (x > 0.54) = P (z > 2)
P (x > 0.54) = 0.9772
In conclusion, the probability that the second sample would be selected with a proportion greater than 0.54 is 0.9772.
