Advanced Placement (AP), 26.02.2021 21:30 glocurlsprinces

The principal of a large high school is concerned about the number of absences for students at his school. To investigate, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. For this population of students, the distribution of absences last month is skewed to the right with a mean of 2.3 and a standard deviation of 1.6. (a) If possible, calculate the probability that a randomly selected student will have 1 or less absences last month. Or, if it’s not possible to calculate this probability, explain why not.

Suppose that a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated.

(b) What is the shape of the sampling distribution of the sample mean? Explain how you know this.

(c) What are the mean and standard deviation of the sampling distribution of the sample mean?

(d) What is the probability that the mean number of absences in a random sample of 50 students is less than 2? Show your work.

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