Question

A study shows that roughly 11% of students are left-handed. If you were to take a sample of 124 students (from a campus with 5000 students), what is the probability that you find more than 15% of students in your sample were left-handed?

a) Define a random variable to be used in the problem. State the distribution of this variable, perform all necessary checks, and state its parameters.

b) What is the probability that you find more than 15% of students in your sample were left-handed?

Answer 1

Solution:

Given:

p=population proportion = 11%=0.11

n=sample size= n = 124

a)

X: Number of left-handed students.

X follows approximately normal distribution with mean μ(p^​) and standard deviation σ(p^​).

Therefore,

μ(p^​)=p=0.11

The conditions are:

So, X follows N(0.11, 0.0281)

b)

We have to find P( > 0.15) = ...?

Using z-score,

So, P(Z>1.42) = 1-P(Z<1.42)

P(Z>1.42) = 1-0.9227 ...Using standard normal table

P(Z>1.42) = 0.0773

Hence, P( > 0.15) = 0.0773

Done