Question 1182031: An exam consists of 50 multiple-choice questions. Based on how much you studied, for any given question you think you have a probability of p=0.70 of getting the correct answer. Consider the sampling distribution of the sample proportion of the 50 questions on which you get the correct answer.
a. Find the mean and standard deviation of the sampling distribution of this proportion.
b.What do you expect for the shape of the sampling distribution? Why?
c. If truly p=0.70, would it be very surprising if you got correct answers on only 60% of the questions? Justify your answer by using the normal distribution to approximate the probability of a sample proportion of 0.60 or less.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! mean is np=50*0.7=35 questions
variance is np(1-p)=35*0.3=10.5
sd is sqrt (V)=3.24 questions
This has a somewhat left skew, because it is asymmetric with the mean to the left of the median. The longer left tail will contribute more to the change to the left of the median than it will the mean,.
z=(0.60-0.70)/sqrt(0.7*0.3/50)
=-0.1/sqrt(0.21/50)
=-1.54
The probability of z's being to the left of -1.54 is 0.0618. It would be a little surprising, but it would not be considered extremely unlikely, either.
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