The marks obtained by the number of students in a certain subject are assumed to be
normally distributed with mean 65 and standard deviation 5. If 3 students are selected
at random from this group, what is the probability that two of them will have marks
over 70?
Answers
Answer:
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Given : The marks obtained by the number of students in a certain subject are assumed to be
normally distributed with mean 65 and standard deviation 5.
3 students are selected at random from this group,
To Find : probability that two of them will have marks over 70
Solution :
Mean = 65
Standard Deviation = 5
Z score = (value - Mean ) / SD
Value = 70
=> Z score = (70 - 65)/5 = 1
Z score 1 means 0.8413
0.8413 portion is below 70
and 1 - 0.8413 = 0.1557 above 70
p = 0.1557 probability that marks above 70
q = 0.8413 probability that marks not above 70
probability that two of three will have marks over 70
n = 3 , x = 2
P(x) = ⁿCₓpˣqⁿ⁻ˣ
= ³C₂(0.1557)²(0.8413)¹
= 0.06
probability that two of them will have marks over 70 = 0.06
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