Question

We believe that 86​% of the population of all Business Statistics I students consider statistics to be an exciting subject. Suppose we randomly and independently selected

21 students from the population. If the true percentage is really 86​%, find the probability of observing 20 or more students who consider statistics to be an exciting subject.

Answer 1

Solution

Given that ,

p = 86% = 0.86

1 - p = 1 - 0.86 = 0.14

n = 21

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

^{P(X 20 ) = P(X = 20 ) + P(X = 21 )}

P() = ((21! /20 ! (21-20)!) * 0.86²⁰ * (0.14)^21-20 + ((21! /21 ! (21-21)!) * 0.86²¹ * (0.14)^21-21

=  ((21! / 20! (1)!) * 0.86²⁰ * (0.14)¹ + ((21! / 20! (0)!) * 0.86²¹ * (0.14)⁰

= 0.1440 + 0.0421

= 0.1861

Probability = 0.1861