Suppose you choose a random sample of size 25 from a large population of tax returns. If the population mean and population standa

Question

Suppose you choose a random sample of size 25 from a large population of tax returns. If the population mean and population standard deviation of the adjusted gross income for these returns are, respectively, $60,000 and $20,000, which of the following is true of the distribution of the sample mean?

Gerda · Answer

The  correct answer  is option  d)   Its mean and standard deviation are $60,000 and $4,000, respectively, regardless of whether the population distribution is normal or not.     Normal distributions  are symmetric and bell-shaped and have same mean, median, and mode.Most members of a normally distributed population have values close to the mean—in a normal population, 96% of the members are within 2 standard deviations of the mean (much better than Chebyshev's 75%).  In any  normally distributed  population, the proportion of members between the mean and one standard deviation below the mean is the same.  here, the standard deviation for 25 samples cannot be $20000. It should be less than that.  Thus, regardless of whether the population distribution is normal or not, the  mean  and  standard deviation  are $60,000 and $4,000, respectively.    To learn more about  normal distribution  refer here  https://brainly.com/question/29509087    #SPJ4    Your question is incomplete, Here is the complete question.  Suppose you choose a random sample of size 25 from a large population of tax returns. If the population mean and population standard deviation of the adjusted gross income for these returns are, respectively, $60,000 and $20,000, which of the following is true of the distribution of the sample mean?  a. Its mean and standard deviation are $60,000 and $20,000, respectively, but only if the population distribution is normal.  b. Its mean and standard deviation are $60,000 and $4,000, respectively, but only if the population distribution is normal.  c. Its mean and standard deviation are $60,000 and $20,000, respectively, regardless of whether the population distribution is normal or not.  d. Its mean and standard deviation are $60,000 and $4,000, respectively, regardless of whether the population distribution is normal or not.

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