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

Answer:

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

Step-by-step 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,

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

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%.