Binomial Distribution Archives

200. Statistics And Probability Answer Library

Assume that when adults with smartphones are randomly selected, 41% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes. Round your answer to four decimal places as needed.

Answer: Given Data: The Probability of Success $(p) = 0.41 $ The Sample Size $(n)=8$ Solution: If 8 adult smartphone users are randomly selected, the probability that exactly 5 of them use their smartphones in meetings or classes: $P(x =…

200. Statistics And Probability Answer Library

A survey found 10% of problems in school were caused by violent actions of students. If a randomly selected sample of 10 school problems were selected, find the probability that more than 2 were caused by violent actions.

Answer: The Probability of success $ (p) = 0.10 $ The Sample size $ (n) = 10 $ Solution: The probability that more than 2 were caused by violent actions: $P(x > 2) = 1 – P(x \leq 2)$ $P(x…

200. Statistics And Probability Answer Library

It has been reported that 70% of college graduates did some sort of volunteer work last year. If 4 college graduates were randomly selected, and x is the number who did volunteer work, determine the following:

Answer:Given data: The probability of success, $p = 0.70$Sample size, $n = 4$ (a) The indicated probability can be calculated by considering binomial distribution as: $P(x = 0) = (nCx) * p^x * (1 – p)^{n – x} $ $P(x…

Discrete and Continuous Probability Distributions

Discrete and Continuous Probability Distributions

Introduction to Probability Distributions A probability distribution is a mathematical description that defines the likelihood of different outcomes in a random process. It tells us the probabilities of various possible outcomes of a random variable. Difference Between Discrete and Continuous…

Basic Probability

Understanding Discrete Random Variables: Basic Concepts

Discrete random variables form a fundamental concept in probability and statistics. Whether you’re analyzing survey results or rolling a die, discrete random variables help quantify the possible outcomes of events that can only take distinct values. In this blog, we’ll…

Binomial Probability Distribution

Thirty-nine percent of U.S. adults have very little confidence in newspapers. You randomly select ten U.S. adults. Find the probability that the number who have very little confidence in newspapers is (1) exactly three.

Answer : Given information : Probability of success $(p) = 0.39$ Sample size $(n) = 10$ Solution : → The probability exactly three : $$P(x = 3) = \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}$$ $$= \binom{10}{3} \cdot 0.39^3 \cdot (1 –…

Binomial Probability Distribution

Thirty-nine percent of U.S. adults have very little confidence in newspapers. You randomly select ten U.S. adults. Find the probability that the number who have very little confidence in newspapers is (a) exactly six

(a) The probability that the number who have very little confidence in newspapers is exactly six is _____. Answer : Given information : Probability of success $(p) = 0.39$ Sample size $(n) = 10$ Solution : → The probability that…

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Understanding Discrete Random Variables and Their Applications in Probability

Understanding Discrete Random Variables and Their Applications in Probability In probability and statistics, a random variable is a fundamental concept that helps us quantify uncertain outcomes. Among these, discrete random variables are those that can take on a finite or…

Binomial Probability Distribution

Determine the indicated probability for a binomial experiment with the given number of trials n=12 and the given success probability p=0.8. Then find the mean, variance, and standard deviation.

a) P(9)= b)$\mu_X$ = c) $\sigma_X^2$ = d) $\sigma_X$ = Answer : Given : Probability of success $(p) = 0.8$ Sample size $(n) = 12$ Solution : a) The probability that x exactly 9 : $$\text{P}(x = 9) = \binom{n}{x}…

Binomial Probability Distribution

Can social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 74% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events.

(a) Out of 30 job listings, at least 21 will conduct social media screening. (b) Out of 30 job listings, fewer than 19 will conduct social media screening. (c) Out of 30 job listings, exactly between 21 and 25 (including…