Question

write the binomial probability in words. then, use a continuity correction to convert the binomial probability to a normal distribution probability.
p(122 < x < 128)
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(121.5 < x < 128.5)
○ b. p(127.5 < x < 128.5)
○ c. p(x > 127.5 or x < 122.5)
○ d. p(122.5 < x < 127.5)
○ e. p(x > 128.5 or x < 121.5)

Explanation:

• For the binomial probability \(P(122 < x < 128)\), in words, it is "the probability of getting a value of \(x\) that is greater than \(122\) and less than \(128\)".
• When using the continuity correction for a binomial - to - normal approximation:
• If \(X\) is a binomial random variable and we are approximating it with a normal random variable \(Y\), for \(P(a < X < b)\) (where \(X\) takes integer values), we use \(P(a + 0.5<Y < b-0.5)\).
• Here \(a = 122\) and \(b = 128\). So, \(a+0.5=122 + 0.5=122.5\) and \(b - 0.5=128-0.5 = 127.5\).

Answer:

• The probability in words: "the probability of getting a value of \(x\) that is greater than \(122\) and less than \(128\)"
• The correct normal probability statement: D. \(P(122.5 < x < 127.5)\)