Question

Rohan appeared for the IITJEE exam and obtained 80 marks on a scale of 150. The scores in IITJEE follow a normal distribution with a mean of 55 and a standard deviation of 12.5. Do you think Rohan will get admitted to IIT?

(a) Yes
(b) No

Answer 1

To determine if Rohan will get admitted to IIT based on his score of 80, we need to calculate the z-score for his score. A z-score of 2 indicates that Rohan's score is 2 standard deviations above the mean. Since the majority of scores lie within 1 to 3 standard deviations from the mean in a normal distribution, it is likely that Rohan will get admitted to IIT.

Step-by-step explanation:

To determine if Rohan will get admitted to IIT based on his score of 80, we need to calculate the z-score for his score.

The formula to calculate z-score is:
z = (x - µ) / σ

Where:
x is the score obtained (80)
µ is the mean (55)
σ is the standard deviation (12.5)

Substituting the values:
z = (80 - 55) / 12.5 = 2

A z-score of 2 indicates that Rohan's score is 2 standard deviations above the mean. Since the majority of scores lie within 1 to 3 standard deviations from the mean in a normal distribution, it is likely that Rohan will get admitted to IIT.

Therefore, the answer is (a) Yes, Rohan will likely get admitted to IIT.