Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x }

Question

Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } < 12 )$ to a normal probability by using the correction for continuity.
A) $\mathrm { P } ( \mathrm { x } < 11.5 )$
B) $\mathrm { P } ( \mathrm { x } > 12.5 )$
C) $P ( x \leq 12.5 )$
D) $P ( x \geq 11.5 )$

Quizplus · Accepted Answer

When converting a binomial probability to a normal probability, the correction for continuity is applied by adjusting the discrete x value to a continuous one. For $P(x < 12)$ in a normal distribution, this translates to $P(x < 11.5)$, because you adjust the boundary to account for the continuous nature of the normal distribution, effectively capturing the probability of "less than 12" by considering anything up to but not including 12.

Ten Percent of the Population Is Left-Handed P(x<12)\mathrm { P } ( \mathrm { x } < 12 )P(x<12)

Ten Percent of the Population Is Left-Handed $\mathrm { P } ( \mathrm { x } < 12 )$