Let us suppose that a particular lecturer manages, with probability 1, to develop exams that have mean 60 and standard deviation 20. The lecturer is teaching two classes, one of size 100 and the other one of size 36, and is about to give an exam to both classes. We treat all students as being independent. Give your answers below in three decimal places. (a) The approximate probability that the average test score in the class of size 100 exceeds 65 is Φ(α), where Φ is the cumulative distribution function of a standard normal random variable. Find the value of α. (b) The approximate probability that the average test score exceeds 65 in the class of size 36 is Φ(β). Find the value of β. (c) Which probability is larger?
Let us suppose that a particular lecturer manages, with
(a) The approximate probability that the average test score in the class of size 100 exceeds 65 is Φ(α), where Φ is the cumulative distribution
(b) The approximate probability that the average test score exceeds 65 in the class of size 36 is Φ(β). Find the value of β.
(c) Which probability is larger?
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