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.
Answers
Step-by-step explanation:
The formula for Z score is given below;
= ( Value - Mean ) / Standard Deviation
As per given information, we put the values for 50 marks
Z score = ( 50 - 40)/8
Z = 5/4 = 1.25
As per given information, we put the values for 60 marks
Z score = ( 60 - 40)/8
Z = 5/2 = 2.5
Let us now find the marks obtained corresponding to standard marks 1.30 and 1.50.
Using the same above formula;
FOR 1.3
1.3 = ( value - 40)/8
Value = 50.4 marks
FOR 1.5
1.5 = ( value - 40)/8
Value = 52 Marks
In terms of standard deviation, the standard marks of students getting 50 and 60 marks are 1.25 and 2.5 respectively.
The marks obtained corresponding to standard marks 1.30 and 1.50 are 50.4 and 52 respectively.
Given:
Number of Candidates = 15000
Mean marks = 40
Standard deviation marks = 8
Step-by-step explanation:
The formula of standard value obtained with mean value and standard deviation is given by the formula:
Standard value = (Value - Mean value)/Standard Deviation
When the marks are 50:
Standard value = (50 - 40)/8 = 10/8
∴ The standard mark when the marks are 50 = 1.25
When the marks are 60:
Standard value = (60 - 40)/8 = 20
∴ The standard mark when the marks are 60 = 2.5
When the standard mark = 1.3
1.3 = (Value - 40)/8
1.3 × 8 = Value - 40
10.4 = Value - 40
∴ Value = 50.4
When the standard mark = 1.5
1.5 = (Value - 40)/8
1.5 × 8 = Value - 40
12 = Value - 40
∴ Value = 52