An exam consists of 50 multiple choice questions. Based on how much you studied,

Question

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 0.65 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50 questions (a) Find the mean and standard error of the sampling distribution of this proportion. Mean0.65 (2 decimal places) Standard error = 0.067 (3 decimal places) (b) What do you expect for the shape of this sampling distribution? approximately normal because np > 15 and nq > 15 approximately normal because n > 30 skewed because p is greater than 0.5 approximately normal because the population is normal (c) If the population proportion p 0.65, what is the probability of getting correct answers on less than 60% of the questions? Probability = (3 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 ) = 0.65
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.65*0.35/50)
=0.0675

c.
P(X < 0.6) = (0.6-0.65)/0.0675
= -0.05/0.0675= -0.7407
= P ( Z <-0.7407) From Standard Normal Table
= 0.2294 ~ 0.230

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