The marks obtained by a number of students in a The marks obtained by a number of students in a certain subject are assumed to be approximately normally distributed with mean 55 and a SD of 5. If 5 students are taken at random from this set, then what is the probability that 3 of them would have scored marks above 60?
Answers
Given : The marks obtained by the number of students in a certain subject are assumed to be
normally distributed with mean 55 and standard deviation 5.
5 students are selected at random from this group,
To Find : probability that 3 of them will have marks over 60
Solution :
Mean = 55
Standard Deviation = 5
Z score = (value - Mean ) / SD
Value = 60
=> Z score = (60 - 55)/5 = 1
Z score 1 means 0.8413
0.8413 portion is below 70
and 1 - 0.8413 = 0.1557 above 60
p = 0.1557 probability that marks above 60
q = 0.8413 probability that marks not above 60
probability that 3 of 5 will have marks over 60
n = 5 , x = 5
P(x) = ⁿCₓpˣqⁿ⁻ˣ
= ⁵C₃(0.1557)³(0.8413)²
= 0.0267
probability that 3 of them will have marks over 60 = 0.0267
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