Question

An entrance examination for admission to a first degree course in medicine was conducted at the
national level. The mean and standard deviation of the marks obtained by 15000 candidates were
40 and 8, respectively. Determine in terms of standard deviation, the standard marks of students
getting 50 and 60 marks. Also find the marks obtained corresponding to standard marks 1.30 and
1.50.

Answer 1

Total number of candidates = 15000

Mean of marks obtained = 40

Standard Deviation (SD) of marks obtained = 8

Now, for 50 marks,

Z score = $\frac{Value-Mean}{SD}$ =  $\frac{50-40}{8}$ = $\frac{10}{8}$ = $\frac{5}{4}$

Then, for 60 Marks,

Z score  =  $\frac{60-40}{8}$ = $\frac{20}{8}$ = $\frac{5}{2}$

∴ SD of students scoring 50 marks = $\frac{5}{4}$ = 1.25

similarly, SD of students scoring 60 marks = $\frac{5}{2}$ = 2.5

Now, for the marks obtained corresponding to the standard marks of 1.30 and 1.50;

1.3 = $\frac{x-40}{8}$

⇒ 10.4 = x - 40

⇒ x = 50.4

similarly,

1.5 =  $\frac{y-40}{8}$

⇒ 12 = y - 40

⇒ y = 52

Ans) a. The SD of the standard marks of the students scoring 50 & 60 marks are 1.25 and 2.5 respectively

b. The marks obtained corresponding to standard marks 1.30 & 1.50 are 50.4 and 52 respectively

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