In 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]

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ESE Electrical 2018 Official Paper
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  1. 36
  2. 23
  3. 12
  4. 10

Answer (Detailed Solution Below)

Option 3 : 12
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Probability 2 D1

Given 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%
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