help me to answer probability questions

Posted on 2014-11-08 07:54:00 in Statistics by SHEKHA

1. In large introductory statistics courses, clicker is commonly used in lectures. For all students enrolled in large introductory statistics courses, their clicker response times have a mean of 1 minute and a standard deviation of 0.2 minutes.

(a) What is the probability that a randomly selected student needs more than 1.2 minutes to answer a clicker question? Do you need to assume a distribution for the response times in order to compute this probability? If so, clearly state what it is. If not, explain why not. (2 marks)

(b) Suppose that the instructor closes the poll for a clicker question whenever he sees that 95% of students have responded. What is the longest time a student can take to respond to a clicker question and have his/her answer recorded (answers submitted after the poll closes will not be recorded)? Do you need to assume a distribution for the response times for this calculation? If so, clearly state what it is. If not, explain why not. (3 marks)

(c) An introductory statistics class has regular group activities where each group consists of four students. What is the probability that a randomly selected group from the class needs more than an average of 1.2 minutes to answer a clicker question? Do you need to assume a distribution for the response times for this calculation? If so, clearly state what it is. If not, explain why not. (3 marks)

(d) A lab section of an introductory statistics course has 30 students. What is the probability that all the students in this lab section needs more than an average of 1.2 minutes to answer a clicker question? Assume that the 30 students are representative of all students enrolled in the course. Do you also need to assume a distribution for the response times for this calculation? If so, clearly state what it is. If not, explain why not. (3 marks)

(e) Consider the following two distributions: (1) the distribution of the response times of 30 students randomly chosen from a course (2) the distribution of the average response time of 30 students randomly chosen from a course Comment on any differences between these two distributions (in terms of their center, spread and shape) and briefly explain why. (4 marks)

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