Answer to Question #349583 in Statistics and Probability for rohit

Question

1.     The results of a particular examination are shown below in summary form:

Result

Percentage of candidates

Passed with distinction

15

Passed without distinction

42

Failed

43

Total

100

 

It is known that a candidate gets failed if he obtains less than 40 marks (out of 100), while he must obtain at least 75 marks in order to pass with distinction. Hence determine the mean and standard deviation of the distribution of the marks, assuming it is of normal type.

Answer 1

$$P(X<40)=P(Z<\dfrac{40-\mu}{\sigma})=0.43$$

$$\dfrac{40-\mu}{\sigma}=-0.1764$$

$$P(X\ge75)=1-P(Z<\dfrac{75-\mu}{\sigma})=0.15$$

$$\dfrac{75-\mu}{\sigma}=1.0364$$

$$\mu=40+0.1764\sigma$$

$$\mu=75-1.0364\sigma$$

$$\sigma=\dfrac{35}{1.2128}\approx28.8588$$

$$\mu=40+0.1764(\dfrac{35}{1.2128})\approx45.0907$$