A test was given to 60 individuals. Half answered 70% of the questions correctly, and the other half answered 90% correctly. Which of the following statements is correct? Group of answer choices Mean < Median Mean = Median Standard Deviation = 0 Mean > Median

Mean = Median.

Step-by-step explanation:

The number of students in the class is, n = 60.

It is provided that half of the students answered 70% of the questions correctly, and the other half answered 90% correctly.

Let X = number of correctly answered questions.

Compute the probability of correctly answering a question as follows:

The random variable X follows a Binomial distribution with parameters n = 60 and p = 0.80.

The mean of the Binomial distribution is:

So the mean of the random variable X is 48.

The median value of a data is the below which 50% of the distribution lies.

Let x denote the median value of the distribution of X.

As,

A normal distribution can be used to approximate the Binomial distribution.

Compute the value of x such that P (X < x) = 0.50 as follows:

The value of z for which P (Z < z) = 0.50 is 0.

The value of x is:

The median value of X is 48.

Thus, Mean = Median.

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