Assume that when adults with smartphones are randomly​ selected, 57​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Assume that when adults with smartphones are randomly​ selected, 57​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes. 

 

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Step 1

Binomial Distribution : 

The binomial probability is a type of discrete probability distribution that can take random values on the range of [0, n], where is the sample size. The main properties of the binomial distribution are :

  • It is discrete, and it can take values from 0 to n, where n is the sample size. 
  • The type of skewness depends on the parameters n and p . 
  • It is determined by two parameters: the population proportion of success, the sample size (or number of trials). 
  • The mean of the binomial distribution is and its standard deviation is np(1p)  .  

It's probability formula is given as: 

            P(X=x) = nx · px·(1-p)n-x 

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