The natural remedy echinacea is reputed to boost the immune system, which will reduce flu and colds. A 6-month study was undertaken to determine whether the remedy works. From this study, the following probability distribution of the number of respiratory infections per year (X) for echinacea users was produced: X 0 1 2 3 4 P (X) 0.343 0.322 0.201 0.076 0.058 Find the following probabilities: A. An echinacea user has more than one infection per year B. An echinacea user has no infections per year C. An echinacea user has between one and three (inclusive) infections per year

Question

Mathematics

Carleen

19 August, 21:43

The natural remedy echinacea is reputed to boost the immune system, which will reduce flu and colds. A 6-month study was undertaken to determine whether the remedy works. From this study, the following probability distribution of the number of respiratory infections per year (X) for echinacea users was produced: X 0 1 2 3 4 P (X) 0.343 0.322 0.201 0.076 0.058 Find the following probabilities: A. An echinacea user has more than one infection per year B. An echinacea user has no infections per year C. An echinacea user has between one and three (inclusive) infections per year

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Answers (1)

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Kassidy Paul · Answer 1

A) 0.335; B) 0.343; C) 0.599

Step-by-step explanation:

For part A,

To find the probability that the user has more than one infection per year, we can either add together the probabilities for 2, 3, 4 and 5; or we can add together the probabilities for 0 and 1 and subtract them from 1:

1 - (P (X = 0) + P (X = 1))

= 1 - (0.343+0.322) = 1-0.665 = 0.335

For part B,

The probability that the user has no infections per year is P (X = 0); this is 0.343.

For part C,

The probability that the user has between 1 and 3 infections (inclusive) per year is

P (1 ≤ X ≤ 3) = 0.322+0.201+0.076 = 0.599