Assume that when adults with smartphones are randomly selected, 55% use them in meetings or classes. If 11 adult smartphone users are randomly selected, find the probability that fewer than 4 of them use their smartphones in meetings or classes. The probability is nothing.

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Assume that when adults with smartphones are randomly​ selected, 55​% use them in meetings or classes. If 11 adult smartphone users are randomly​ selected, find the probability that fewer than 4 of them use their smartphones in meetings or classes.  The probability is nothing.

stomachdm · Accepted Answer

Let X denote the number of smartphone users who use their smartphones in meetings or classes and X follows Binomial distribution with number of trials&amp;nbsp;n=11&amp;nbsp;and probability of success&amp;nbsp;p=0.55.Probability mass function of Binomial variable&amp;nbsp;P(X=x)=nCxpx(1−p)n−xP(X&amp;lt;4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=11C0(0.55)0(1−0.55)11−0+11C1(0.55)1(1−0.55)11−1+11C2(0.55)2(1−0.55)11−2+11C3(0.55)3(1−0.55)11−3=1×1×0.0001532278301+11×0.55×0.0003405062892+55×0.3025×0.0007566806426+165×0.166375×0.001681512539=0.0001532278301+0.00206006305+0.01258927419+0.04616067203=0.0609632371≈0.0610&amp;nbsp;(answer)

sonSnubsreose6v · Accepted Answer

This is a binomial with n=7 p=0.55   a least 4 of them use their smartphones that is 1-prob(3) of them use them.   =0.6083 is answer.   probability 4 use them is 7C4⋅0.554⋅0.453=0.2918   for 5 it is 0.2140   for 6 it is 0.0872   for 7 it is 0.557 or 0.0152   add them to get 0.6082 (rounding error)

nick1337 · Accepted Answer

The number of adults who use smartphones is the variable x, according to the data.A random sample of adults using smartphones is taken into account using the information provided.There are two possible results based on the information provided: &quot;using smart phones in meetings&quot; and &quot;using smart phones in classrooms.&quot; This suggests that the initial condition for the binomial distribution is met.11 adult Smartphone users who were chosen at random are also taken into account. In other words, it is known in advance how many trials will be performed in the experiment. It follows from this that the second prerequisite for the binomial distribution is met.Because each variable operates independently of the others, the trails (adult) are independent. It follows from this that the third condition for the binomial distribution is met.According to the statistics provided, the school estimates that 55% of people utilize them in meetings or classrooms, representing a success probability that remains constant throughout the experiment. It follows from this that the fourth prerequisite for the binomial distribution is met.Therefore, the distribution is binomial distribution with sample size 11 and probability of success 0.55. That is,&amp;nbsp;X∼Binomial(11,0.55)The probability that fewer than 4 of them use their smartphones in meetings or classes is obtained below:The required probability is,P(X&amp;lt;4)=[P(X=0)+P(X=1)+P(X=2)+P(X=3)]=[(110)(0.55)0(1−0.55)11−0+(111)(0.55)1(1−0.55)11−1+(112)(0.55)2(1−0.55)11−2+(113)(0.55)3(1−0.55)11−3]=[0.0002+0.0021+0.0126+0.0462]=0.0611

Assume that when adults with smartphones are randomly selected, 55%

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