Question

What is the sampling distribution

Answer 1

The normal approximation of the binomial distribution can be used where
\[\mu=np=100 \times 0.1=10\]
and
\[\sigma=\sqrt{np(1-p)}=3\]
A. The z-score for 14 left handed students is
\[z=\frac{X-\mu}{\sigma}=\frac{14-10}{3}=1.3333\]
Reference to standard normal distribution table shows the probability that 14% or more of the sample is left handed is 1.0000 - 0.9088 = 0.0912

B. The z-score for fewer than 8 students in the sample being left handed is
\[z=\frac{7-10+0.5}{3}=-0.8333\]
where the term 0.5 is a correction caused by the change from a discrete to a continuous distribution.
Reference to standard normal distribution table shows the required probability is 0.2022