Question

write the binomial probability in words. then, use a continuity correction to convert the binomial probability to a normal distribution probability.
p(64 < x < 73)
write the probability in words.
the probability of getting
which of the following is the normal probability statement that corresponds to the binomial probability statement?
a. p(x > 73.5 or x < 63.5)
b. p(63.5 < x < 73.5)
c. p(72.5 < x < 73.5)
d. p(x > 72.5 or x < 64.5)
e. p(64.5 < x < 72.5)

Explanation:

Step1: Interpret binomial probability in words

The binomial probability \(P(64 < x < 73)\) means the probability that the number of successes \(x\) is greater than \(64\) and less than \(73\).

Step2: Apply continuity correction

For a binomial random variable \(x\) (discrete) being approximated by a normal random variable (continuous), when we have \(aHere \(a = 64\) and \(b = 73\), so \(a+0.5=64 + 0.5=64.5\) and \(b - 0.5=73-0.5 = 72.5\)

Answer:

The probability of getting a value of \(x\) that is greater than \(64\) and less than \(73\).
E. \(P(64.5 < x < 72.5)\)