Question

According to a survey, 58% of people carry at least 1 reusable water bottle. If 5 people are selected randomly, what is the probability that at least 4 of them will be carrying a reusable water bottle? Round your answer to the nearest tenth of a percent.

Answer 1

The probability that at least 4 of them will be carrying a reusable water bottle is 30.3%.

Explanation:

Here it is given that probability of people who carry at least 1 reusable water bottle is p = 0.58.

A random sample of n = 5 people are selected.

This data follows binomial distribution, with success denoted by a a person carrying t least 1 reusable water bottle. The probability mass function of binomial distribution is,

`P(X=x)={n\choose x}\ p^(x)\ (1-p)^(n-x)\ ;\ x=0,1,2,3...,\ 0<p<1`

Compute the probability that at least 4 of them will be carrying a reusable water bottle as follows:

P (X ≥ 4) = P (X = 4) + P (X = 5)

`={5\choose 4}\ 0.58^(4)\ (1-0.58)^(5-4)+{5\choose 5}\ 0.58^(5)\ (1-0.58)^(5-5)\\=0.237646416+0.0656356768\\=0.3032820928\\\approx 0.3033`

The percentage is, 0.3033 × 100 = 30.3%.

Thus, the probability that at least 4 of them will be carrying a reusable water bottle is 30.3%.