Question

a particular test has 72% pass rate. A teacher decides to grade test until 15. People have passed before stopping for a break. let X equals a number of test graded before taking a break. determine if X is binomial by stating and checking all four requirements. if X is binomial summarize the distribution of X in shorthand notation.

Answer 1

Answer: To determine if X is a binomial random variable, we need to check the following four requirements:

The trials are independent: Assuming that each test is graded independently of the others, this requirement is satisfied.

There are only two outcomes: Pass or fail.

The probability of success is constant: The probability of passing is 0.72 for each test.

The sample size is fixed: The teacher is grading 15 tests.

All four requirements are satisfied, so X is a binomial random variable.

We can summarize the distribution of X using the shorthand notation:

X ~ Bin(n = 15, p = 0.72)

This means that X is a binomial random variable with 15 trials and a probability of success (passing) of 0.72.

Explanation: