Question

Refer to the accompanying Minitab display. (When blood donors were randomly selected, $45 \%$ of them bad blood that is Group O (based on data from the Greater New York Blood Program).) The display shows the probabilities obtained by entering the values of $n=5$ and $p=0.45$ Find the probability that at most 2 of the 5 donors have Group O blood.

Name: Problem 28, Chapter 5: Elementary Statistics
Uploaded: 2023-03-21T16:33:31-08:00
Duration: 1 min 37 s
Channel: Prabhakar Kumar
Description: Refer to the accompanying Minitab display. (When blood donors were randomly selected, 45 % of them bad blood that is Group O (based on data from the Greater New York Blood Program).) The display shows the probabilities obtained by entering the values of n=5 and p=0.45 Find the probability that at most 2 of the 5 donors have Group O blood.

   Refer to the accompanying Minitab display. (When blood donors were randomly selected, $45 \%$ of them bad blood that is Group O (based on data from the Greater New York Blood Program).) The display shows the probabilities obtained by entering the values of $n=5$ and $p=0.45$
Find the probability that at most 2 of the 5 donors have Group O blood.

Elementary Statistics

Mario F. Triola 11th Edition

Chapter 5, Problem 28

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Solved by Expert Prabhakar Kumar

03/21/2023

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45. We are asked to find the probability that at most 2 of the 5 donors have Group O blood. This can be written as P(X ≤ 2). Show more…

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Refer to the accompanying Minitab display. (When blood donors were randomly selected, $45 \%$ of them bad blood that is Group O (based on data from the Greater New York Blood Program).) The display shows the probabilities obtained by entering the values of $n=5$ and $p=0.45$ Find the probability that at most 2 of the 5 donors have Group O blood.

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Key Concepts

Cumulative Probability

This concept represents the probability that a random variable takes a value less than or equal to a given threshold. In the context of the binomial distribution, it is obtained by summing the probabilities of all outcomes from 0 up to the threshold value, such as calculating the probability of at most 2 successes.

Binomial Distribution

This is a probability distribution used for modeling the number of successes in a fixed number of independent trials, where each trial has two outcomes (success or failure) and the probability of success remains constant. It is characterized by the parameters n (number of trials) and p (probability of success).

Probability Mass Function

This function gives the probability that a discrete random variable is exactly equal to some value. For the binomial distribution, it involves calculating the probability of exactly k successes in n trials using the binomial coefficient and the formula p^k * (1-p)^(n-k).

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