Question

write the binomial probability in words. then, use a continuity correction to convert the binomial probability to a normal distribution probability.
p(x ≥ 109)
write the probability in words.
the probability of getting 109 successes.
which of the following is the normal probability statement that corresponds to the binomial probability statement?
○ a. p(108.5 < x < 109.5)
○ b. p(x < 109.5)
○ c. p(x > 108.5)
○ d. p(x < 108.5)
○ e. p(x > 109.5)

Explanation:

Step1: Analyze the binomial probability in words

The binomial probability \(P(x\geq109)\) means the probability of getting at least 109 successes.

Step2: Apply the continuity correction

When converting a binomial probability \(P(x\geq n)\) (where \(n = 109\)) to a normal distribution probability, we use the continuity correction. For \(P(x\geq n)\), we rewrite it as \(P(x>n - 0.5)\). Substituting \(n = 109\), we get \(P(x>109 - 0.5)=P(x > 108.5)\)

Answer:

The probability of getting at least 109 successes.
C. \(P(x>108.5)\)