Assuming that all conditions are met to approximate a binomial probability distribution with the standard normal distribution, then to compute $P ( 12 \leq x \leq 15 )$ from the binomial distribution we must compute as the normal approximation. A) $\mathrm { P } ( 11.5

Question

Assuming that all conditions are met to approximate a binomial probability distribution with the standard normal distribution, then to compute $P ( 12 \leq x \leq 15 )$ from the binomial distribution we must compute as the normal approximation. A) $\mathrm { P } ( 11.5 < \mathrm { x } < 15.5 )$ B) $\mathrm { P } ( 12.5 < \mathrm { x } < 14.5 )$ C) $\mathrm { P } ( \mathrm { x } > 15.5 ) \text { and } \mathrm { P } ( \mathrm { x } < 11.5 )$ D) $\mathrm { P } ( \mathrm { x } > 12.5 ) \text { and } \mathrm { P } ( \mathrm { x } < 14.5 )$

Quizplus · Accepted Answer

When approximating a binomial distribution with a normal distribution, continuity correction is applied by adjusting the binomial range by 0.5 in each direction. Thus, for $P(12 \leq x \leq 15)$, the equivalent normal approximation is $P(11.5 < x < 15.5)$.

Assuming That All Conditions Are Met to Approximate a Binomial P(12≤x≤15)P ( 12 \leq x \leq 15 )P(12≤x≤15)

Assuming That All Conditions Are Met to Approximate a Binomial $P ( 12 \leq x \leq 15 )$