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# Answer to Question #44957 in Statistics and Probability for Pranav V K

Question #44957
The marks obtained by a number of students in a certain subject are approximately normally distributed with mean 65 and standard deviation 5. If 3 students are selected at random from this group, what is the probability that at least 1 of them would have scored above 75?

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Assignment Expert
25.08.14, 21:46

Dear THIRUNAV

THIRUNAV
17.08.14, 09:10

If X represents the marks obtained by the students, X ~Normal (65, 5)
P (A student scores above 75) = P(X>75) = P ((75-65)/5 < (X-65)/5 <∞)
= P(2<Z<∞), where Z-standard normal variate
= 0.5-0.4772, (0.4772 table value we have to refer Z table
P (A student scores above 75) = 0.0228 then q=0.9772
using binomial distn you can get the answer ((0..0677)