(c) With the information given, are you able to calculate the probability that a randomly- selected group of 10 students will have a mean score above 60 points? (d) What would you have to assume about the distribution of the exam scores in order to answer part (c)? Make your assumption(s) and calculate your answer. (e) With the information given, are you able to calculate the probability that a randomly- of 100 students will have a mean score above 60 points? selected group (f) What would you have to assume about the distribution of the exam scores in order to answer part. (e)? Make vour assumption(s) and calculate vour answer

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use #8 for reference but answer #9 d, e , f only

**Statistics 230 - Homework Assignments**

8. Susan and Olivia both took an introductory statistics class; however, Susan attends University A and Olivia attends University B. The final exam for University A has a mean (\(\mu\)) of 50 and a standard deviation (\(\sigma\)) of 10, while Susan scored 62 points. The final exam for University B has a mean (\(\mu\)) of 1500 and a standard deviation (\(\sigma\)) of 25, and Olivia scored 1540 points. We want to know who understands statistics better by comparing Susan’s and Olivia’s final exam scores. Assuming the student body at each university is comparable, who performed better on the final exam? Explain.

9. Assume we are looking at University A’s final exam (from the previous problem).

   (a) With the information given, are you able to calculate the probability of a randomly selected student scoring higher than 60 points?

   (b) What would you have to assume about the distribution of the exam scores in order to answer part (a)? Make your assumption(s) and calculate your answer.

   (c) With the information given, are you able to calculate the probability that a randomly-selected group of 10 students will have a mean score above 60 points?

   (d) What would you have to assume about the distribution of the exam scores in order to answer part (c)? Make your assumption(s) and calculate your answer.

   (e) With the information given, are you able to calculate the probability that a randomly-selected group of 100 students will have a mean score above 60 points?

   (f) What would you have to assume about the distribution of the exam scores in order to answer part (e)? Make your assumption(s) and calculate your answer.

---

This text sets up a statistical analysis problem comparing the performances of two students from different universities, with exercises focusing on calculating probabilities using given statistics. Students are tasked with making assumptions about distributions to solve these problems.
Transcribed Image Text:**Statistics 230 - Homework Assignments** 8. Susan and Olivia both took an introductory statistics class; however, Susan attends University A and Olivia attends University B. The final exam for University A has a mean (\(\mu\)) of 50 and a standard deviation (\(\sigma\)) of 10, while Susan scored 62 points. The final exam for University B has a mean (\(\mu\)) of 1500 and a standard deviation (\(\sigma\)) of 25, and Olivia scored 1540 points. We want to know who understands statistics better by comparing Susan’s and Olivia’s final exam scores. Assuming the student body at each university is comparable, who performed better on the final exam? Explain. 9. Assume we are looking at University A’s final exam (from the previous problem). (a) With the information given, are you able to calculate the probability of a randomly selected student scoring higher than 60 points? (b) What would you have to assume about the distribution of the exam scores in order to answer part (a)? Make your assumption(s) and calculate your answer. (c) With the information given, are you able to calculate the probability that a randomly-selected group of 10 students will have a mean score above 60 points? (d) What would you have to assume about the distribution of the exam scores in order to answer part (c)? Make your assumption(s) and calculate your answer. (e) With the information given, are you able to calculate the probability that a randomly-selected group of 100 students will have a mean score above 60 points? (f) What would you have to assume about the distribution of the exam scores in order to answer part (e)? Make your assumption(s) and calculate your answer. --- This text sets up a statistical analysis problem comparing the performances of two students from different universities, with exercises focusing on calculating probabilities using given statistics. Students are tasked with making assumptions about distributions to solve these problems.
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