Ten percent of the population is lefthanded A class of 9250

Ten percent of the population is left-handed. A class of 9250 students is selected. Convert the binomial probability P(x<12) to a normal probability by using the correction for continuity.

Solution

A continuity correction factor is used when you use a continuous function to approximate a discrete one. In simple terms, you use it when you want to approximate a binomial with a normal distribution. According to the Central Limit Theorem, the sample mean of a distribution becomes approximately normal if the sample size is large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p is at least 5.

Here n=9250

p=.1

Now,np=9250*.1 =925

Continuity correction factor table

If P(X=n) use P(n – 0.5 < X < n + 0.5)
If P(X>n) use P(X > n + 0.5)
If P(Xn) use P(X < n + 0.5)
If P (X<n) use P(X < n – 0.5)
If P(X n) use P(X > n – 0.5)

Here in our problrem we have to find P(X<12) so according to the table the continuity correction is P(<12-.5)=>P(X<11.5) -answer