Question

In: Statistics and Probability

True or False. In order to use results from the Central Limit Theorem for calculating that...

True or False.

  1. In order to use results from the Central Limit Theorem for calculating that the sample mean is greater than some number, the population you are sampling from must have a normal distribution.
  2. If a variable has a binomial distribution with the probability of success equal to 0.82, then the distribution is skewed to the left.
  3. For calculating the probability that a sample mean is greater than some given value, in solving this problem, one of the first things you would do is to apply the continuity correction.
  4. If you took many samples (size >50) from a population and calculated the proportion for each of the samples, then the distribution of these proportions would have an approximate normal distribution.
  5. If a person had a z-score of 0.49, this indicates their actual raw score is close to the 50th percentile.
  6. If the sample size is equal to 40 and the true proportion is equal to 0.25, then the z-distribution can be used instead of the binomial distribution for calculating probabilities.

7.The approximation to normality for the sampling distribution of * becomes better and better as the sample size increases.

  1. When sampling from a normal distribution where the mean = g and variance 6 , then the sampling distribution for R will also have a mean = g and a variance = 62 .

Solutions

Expert Solution

  1. In order to use results from the Central Limit Theorem for calculating that the sample mean is greater than some number, the population you are sampling from must have a normal distribution.

True

  1. If a variable has a binomial distribution with the probability of success equal to 0.82, then the distribution is skewed to the left.

False

  1. For calculating the probability that a sample mean is greater than some given value, in solving this problem, one of the first things you would do is to apply the continuity correction.

False

  1. If you took many samples (size >50) from a population and calculated the proportion for each of the samples, then the distribution of these proportions would have an approximate normal distribution.

False

  1. If a person had a z-score of 0.49, this indicates their actual raw score is close to the 50th percentile.

False

  1. If the sample size is equal to 40 and the true proportion is equal to 0.25, then the z-distribution can be used instead of the binomial distribution for calculating probabilities.

True

7.The approximation to normality for the sampling distribution of * becomes better and better as the sample size increases.

True

  1. When sampling from a normal distribution where the mean = g and variance 6 , then the sampling distribution for R will also have a mean = g and a variance = 62 .

False

orchestra answered 1 year ago
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