Answer:
<em>Mean = Median</em>.
Step-by-step explanation:
The number of students in the class is, <em>n</em> = 60.
It is provided that half of the students answered 70% of the questions correctly, and the other half answered 90% correctly.
Let <em>X</em> = number of correctly answered questions.
Compute the probability of correctly answering a question as follows:
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 60 and <em>p</em> = 0.80.
The mean of the Binomial distribution is:
So the mean of the random variable <em>X</em> is 48.
The median value of a data is the below which 50% of the distribution lies.
Let <em>x</em> denote the median value of the distribution of <em>X</em>.
As,
- np = 48 > 10
- n (1 - p) = 60 × (1 - 0.80) = 12 > 10
A normal distribution can be used to approximate the Binomial distribution.
Compute the value of <em>x</em> such that P (X < x) = 0.50 as follows:
The value of <em>z</em> for which P (Z < z) = 0.50 is 0.
The value of <em>x</em> is:
The median value of <em>X</em> is 48.
Thus, Mean = Median.