Recently the U.S. Department of Education released a report on online learning s
ID: 3336783 • Letter: R
Question
Recently the U.S. Department of Education released a report on online learning stating that blended instruction, a combination of conventional face-to-face and online instruction, appears more effective in terms of student performance than conventional teaching. You decide to poll the incoming students at your institution to see if they prefer courses that blend face-to-face instruction with online components. In an SRS of 400 incomingstudents, you find that 315 prefer this type of course.
(c) Using the 68–95–99.7 rule, if you had drawn an SRS from the United States, you would expect p to fall between what two percents about 95% of the time? (Round your answers to two decimal places.)
Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
proportion ( p ) = 0.7875
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.7875*0.2125/400)
=0.0205
95% OF DATA
About 95% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 2s.d)
So to the given normal distribution about 95% of the observations lie in between
= [0.7875 ± 2 * 0.0205]
= [ 0.7875 - 2 * 0.0205 , 0.7875 + 2* 0.0205]
= [ 0.7465 , 0.8285 ]
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