Question
Download Solution PDFIn a sample of 100 students, the mean of the marks (only integers) obtained by them in a test is 14 with its standard deviation 2.5 [marks obtained can be fitted with a normal distribution]. The percentage of students scoring 16 marks is_____(find approximate value).
[Consider Area under standard Normal curve between z = 0 & z = 0.6 is 0.2257 and between z = 0 and z = 1.0 is 0.3413]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven that μ = 14, σ = 2.5
P(x = 16) = P(15.5 < × < 16.5)
\(= P\left( {\frac{{15.5 - u}}{\sigma } < \frac{{x - u}}{\sigma } < \frac{{16.5 - u}}{{2.5}}} \right)\)
\(= P\left( {\frac{{15.5 - u}}{{2.5}} < z < \frac{{16.5 - u}}{{2.5}}} \right)\)
= P(0.6 < z < 1)
= Area of OABCDE – Area of OADE
= 0.3413 – 0.2257 = 0.1156
% age of students = 100 × 0.1156
= 11.5 ∼ 12%Last updated on Jul 2, 2025
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