A company provides tuition for mathematics students across the country. It provides two levels of tuition: tuition

for general-level students and tuition for advanced-level students. All students who receive tuition at this company must first complete a test, to assess their initial comprehension of mathematics.

For general-level students, the population mean score in this test is 50.97, with a population standard deviation of 11.74. For advanced students, the population mean score in the test is 81.08, with a population standard deviation of 14.57.

A statistician wants to study the results of a random selection of general students and a random selection of advanced students. The statistician intends to draw a sample of 50 general-level students and a sample of 200 advanced-level students.

a)From the following list, select the statements that are true. For each statement, assume that all other measures remain constant in that instance.

  The larger a population mean, the greater the variation in sample means for samples from that population.
  The smaller a population mean, the greater the variation in sample means for samples from that population.
  The larger a population variance, the greater the variation in sample means for samples from that population.
  The smaller a population variance, the greater the variation in sample means for samples from that population.
  The larger the sample size for samples from a population, the greater the variation in sample means.
  The smaller the sample size for samples from a population, the greater the variation in sample means.

b)For the samples described in the scenario above, the sample mean scores for samples of general-level students will have a higherlower level of variation than the variation in sample mean scores for samples of advanced-level students.

Your parents are always complaining that you do not do enough housework. They say that you should be helping them out because you are only a student and you have a lot more spare time than them.

The number of hours per week that your parents work has a mean of 48.36 hours and a standard deviation of 2.47 hours. You believe that the number of hours per week that you have to study for university has a mean of 47.83 hours and a standard deviation of 2.90 hours.

You plan to record the number of hours that you study each week over 20 randomly selected weeks throughout the year. Calculate the probability that the mean of your sample is greater than the mean number of hours per week worked by your parents. You may find this standard normal table useful. Give your answer as a decimal to 4 decimal places.

probability = 

A company records the number of angry calls made to a particular department every working day. It then takes the average of these numbers over 10 working days. This average is based in the assumption that the distribution of the number of angry calls on a particular day is unaffected by the day on which the call is received.

The probability that this average is greater than 27 is 5%. Calculate the mean number of angry calls on any particular day if you know that the standard deviation of the number of angry calls per day is 14. You may find this standard normal table useful. Give your answer to 3 decimal places.

Mean number of angry calls per day = 

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