### Probability Question: Knowledgeable Football Fans**Problem Statement:**Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans.**Multiple Choice Options:**- A. 0.059- B. 0.204- C. 0.417- D. 0.650This question can be approached using the binomial probability formula, which is used to compute the probability of exactly \( k \) successes (in this case, five men considering themselves knowledgeable football fans) out of \( n \) trials (in this case, 12 randomly selected men), given the probability \( p \) of success on a single trial.#### Explanation of the Binomial Probability Formula:\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]Where:- \( n \) = 12 (number of trials)- \( k \) = 5 (number of successes)- \( p \) = 0.65 (probability of success)- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \)##### Steps to Calculate:1. **Calculate the Binomial Coefficient**: \[ \binom{12}{5} = \frac{12!}{5!(12-5)!} \]2. **Calculate the Probability**: \[ P(X = 5) = \binom{12}{5} \cdot (0.65)^5 \cdot (0.35)^7 \]Using these steps and probability calculations, one arrives at the final answer, which corresponds to one of the multiple-choice options provided.This problem serves as an excellent exercise in understanding how to apply binomial probability in practical scenarios and interpret statistical data accurately.

Answered: Image /qna-images/answer/200de128-0619-4cfd-97fa-a2cca5c277ab.jpg

Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans. O A. 0.059 O B. 0.204 O C. 0.417 OD. 0.650

Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans. O A. 0.059 O B. 0.204 O C. 0.417 OD. 0.650

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

66% of all violent felons in the prison system are repeat offenders. If 34 violent felons are randomly selected, find the probability that a. Exactly 24 of them are repeat offenders. b. At most 22 of them are repeat offenders. c. At least 20 of them are repeat offenders. d. Between 21 and 25 (including 21 and 25) of them are repeat offenders.
A dormitory on campus houses 100 students. 42 are male, and 40% are KINE majors. A student is selected at random. The probability of selecting a female, and a KINE major? Provide either a percentage (1 decimal) or a fraction with three decimal places. Answer:
48% of all violent felons in the prison system are repeat offenders. If 38 violent felons are randomly selected, find the probability that a. Exactly 17 of them are repeat offenders. b. At most 17 of them are repeat offenders. c. At least 17 of them are repeat offenders. d. Between 14 and 20 (including 14 and 20) of them are repeat offenders.
UK.5.
60% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 44 owned dogs are randomly selected, find the probability thata. Exactly 27 of them are spayed or neutered. b. At most 29 of them are spayed or neutered. c. At least 27 of them are spayed or neutered. d. Between 26 and 33 (including 26 and 33) of them are spayed or neutered.
Suppose that in basketball you are successful on 71% of your free throw attempts. You take 16 free throws. Round your answers to three decimals if needed. a. How many of the attempts do you expect will be successful? b. What is the probability that you will make between (inclusive) 9 and 11 free throws? c. What is the probability that you make all your attempts? Submit Question or
Suppose that a screening test diagnoses 90% of sick people positive and 90% of healthy people negative. Assume that 15% of those screened are sick. If a screened person is chosen at random, then the probability of having a negative diagnosis is: O a. 0.78 b. 0.0192 C. 0.981 O d. 0.109 O e. 0.22
Submit your answer as an exact fraction or a decimal rounded to the hundredths place. Cupcakes are being randomly passed out to every student in the class. The assortment of cupcakes is described in the table below. What is the probability of receiving a cupcake that is not vanilla flavored? Cupcake flavor Number of cupcakes Vanilla 7 Mint chocolate 3 Red velvet 4 Carrot Cake 6
48% of all violent felons in the prison system are repeat offenders. If 44 violent felons are randomly selected, find the probability that a. Exactly 18 of them are repeat offenders. Correct b. At most 20 of them are repeat offenders. c. At least 19 of them are repeat offenders. d. Between 14 and 19 (including 14 and 19) of them are repeat offenders.
A poll showed that 44.5% of Americans say they believe that life exists elsewhere in the galaxy. What is the probability (in percent form) of randomly selecting someone who does not believe that life exists elsewhere in the galaxy. Probability = % (Please round your answer to one decimal place.) %3D Submit Question 17,123 NOV 1 16 tv MacBook Air 80 888 F3 F4 F5 F6 F7
55% of all violent felons in the prison system are repeat offenders. If 38 violent felons are randomly selected, find the probability that a. Exactly 22 of them are repeat offenders. b. At most 20 of them are repeat offenders. c. At least 20 of them are repeat offenders. d. Between 18 and 23 (including 18 and 23) of them are repeat offenders.
61% of all violent felons in the prison system are repeat offenders. If 41 violent felons are randomly selected, find the probability that a. Exactly 24 of them are repeat offenders. b. At most 26 of them are repeat offenders. c. At least 22 of them are repeat offenders. d. Between 22 and 27 (including 22 and 27) of them are repeat offenders.