Question

ten percent of the population is left - handed. a class of 100 students is selected. convert the binomial probability ( p(x<12) ) to a normal probability by using the correction for continuity.

a. ( p(x<11.5) )
b. ( p(xgeq11.5) )
c. ( p(xleq12.5) )
d. ( p(x>12.5) )

Explanation:

Step1: Understand the correction for continuity

When converting a binomial probability \(P(X < k)\) to a normal probability, we use the correction for continuity. For \(P(X < k)\), we adjust to \(P(X < k - 0.5)\).

Step2: Apply the correction

Here \(k = 12\). So \(k-0.5=12 - 0.5=11.5\). Thus \(P(X < 12)\) is converted to \(P(X < 11.5)\) using the correction for continuity.

Answer:

A. \(P(x < 11.5)\)