Question

About 12% of individuals write with their left hands. If a class of 130 students meets in a classroom with 130 individual desks, and 14 of the students write with their left hands, the probability that not all left handed students will have access to a special desk, constructed for people who write with their left hands is _______

Answer 1

0.1019

Explanation:

Probability, p=12%=0.12

Sample size, n=130 students

Those writing with left=14 students

Using the formula for binomial distribution

P(X≤x)=
`\left[\begin{array}{}n\\x\end{array}\right]p^(x)(1-p)^(n-x)`

Substituting 0.12 for p, 130 for n, 14 for x we obtain

P(X≤x)=
`\left[\begin{array}{}130\\14\end{array}\right]0.12^(14)(1-0.12)^(130-14)`

P(X≤x)=
`130C14*0.12^(14)(0.88)^(116)`

P(X≤x)=0.1019