# Skewed Distribution and Sampling (Multi Choice)

The amount of time that it takes to take an exam has a skewed-to-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes. A sample of 64 students will be selected at random. A. Which of the following properly describes the distribution of the amount of time it takes to take an exam? aa)N(65,8) bb) N(65,1) cc) A skewed distribution with a mean of 65 minutes, but unknown variance.dd) A skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes.

B. Which of the following properly describes the sampling distribution of the sample mean? aa) Approximately N(65,8) bb) N(65,1) cc) approximately N(1,65) dd) skewed distribution with a mean of 65 and a standard deviation of 1.

C.If we decide to choose a random sample of 9 students, instead of 64 students, which of the following properly describes the sampling distribution of the sample mean for 9 students? aa) It is the distribution of a data set of 9 students time. bb) It is normally distributed. cc) Its distribution has a mean of 65 minutes and a standard deviation of 8/3 minutes, but the shape of the distribution may not be normal. dd) Its distribution may not be normal, but the distribution mean is less the 65 minutes.

D. Which of the following is correct for the sampling distributions of the sample mean when sample size=9? aa) The sampling distribution has a center at 8 minutes. bb) The sampling distribution has a center of 65 minutes. cc) The sampling distribution has standard deviation 8 minutes. dd) The sampling distribution has a standard deviation 65 minutes.

E. Which of the following is correct for estimating unknown population mean using sample mean? aa) The sample mean is always equal to the population mean, regadless of sample size. bb) The sample mean can not be used to estimate the population mean. cc) The sample mean will better estimate the population mean if the sample size is larger. dd)None of the above.

Please explain your solutions and add any comment that might be helpful.

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#### Solution Preview

A)N(65,1) : Standard Dev of sample = Std Dev of population/ sqrt(sample size)

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<br>B)dd) skewed distribution with a mean of 65 and a ...