Question

write the binomial probability in words. then, use a continuity correction to convert the binomial probability to a normal distribution probability.
p(x ≥ 80)
write the probability in words.
the probability of getting 80 successes.
which of the following is the normal probability statement that corresponds to the binomial probability statement?
a. p(x < 79.5)
b. p(x > 80.5)
c. p(x > 79.5)
d. p(79.5 < x < 80.5)
e. p(x < 80.5)

Explanation:

Step1: Understand the binomial probability statement

The binomial probability \(P(x\geq80)\) means the probability of getting 80 or more successes.

Step2: Apply continuity correction

For a binomial \(x\) (discrete) to normal \(X\) (continuous) conversion, when we have \(x\geq n\) (discrete), the continuity - corrected normal probability is \(P(X > n - 0.5)\). Here \(n = 80\), so we get \(P(X>79.5)\).

Answer:

The probability of getting 80 or more successes. C. \(P(x > 79.5)\)