Question

Approximate the following binomial probability by the use of normal approximation. Twenty percent of students who finish high school do not go to college. What is the probability that in a sample of 80 high school students, 10 or less will not go to college? (Enter as a decimal rounding to 3 decimal places).

Answer 1

The number of high school students out of 80 who do not goto college here is modelled as:

This is approximated to a normal distribution here as:

The probability here is computed as:

P(X <= 10)

Using the continuity correction here, we get:

P(X < 10.5)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we get here:

Therefore 0.062 is the required probability here.