Sampling Distribution

1. A die is rolled 180 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 20 times,what is the standard deviation of the normal distribution that you would use in this case

2. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

3. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled exactly 100 times. You need to find the probability that X=100. Explain how you would use continuity correction in this case.

4. What is the name of the theorem that states that the sampling distribution of the sample mean is approximately normal when the sample is large?

5. Determine whether the following random variables have a binomial distribution:

A) Ten students are chosen from a statistics class (with replacement) of 400 students. Let X be the number of students who passed the class.

B) A die is tossed three times. Let X be the sum of the three numbers obtained.

C) A coin is tossed until a head appears. Let X be the number of tosses.

only A is a binomial distribution

only B is a binomial distribution

only C is a binomial distribution

only A and B is a binomial distribution

only A and C is a binomial distribution

only B and C is a binomial distribution

all A, B, and C are binomial distributions

none is a binomial