Sixty-eight percent of adults would still consider a car brand despite product/safety recalls. You randomly select 20 adults. Find the probability that the number of adults that would still consider a car brand despite product/safety recalls is at most one. Distribution type: ? Probability: ?

Question

Sixty-eight percent of adults would still consider a car brand despite product/safety recalls. You randomly select 20 adults.  Find the probability that the number of adults that would still consider a car brand despite product/safety recalls is at most one.   Distribution type: ? Probability: ?

diskusje5 · Accepted Answer

Step 1&amp;nbsp;We have data:p=0.68&amp;nbsp;n=20&amp;nbsp;The distribution that is described is a binomial distribution since the outcomes—success and failure—are binary in nature. The probability that each trial will be successful or unsuccessful is equivalent to the probability that, at most, one adult will continue to select a specific automobile brand notwithstanding product or safety recalls.Applying Binomial theorem&amp;nbsp;Probability of x success out of n trial is given by&amp;nbsp;P(X=x)=(beg∈{array}{c}n∖xend{array})×px×(1−p)n−x&amp;nbsp;⇒P(X≤1)=P(X=0)+P(X=1)&amp;nbsp;⇒(beg∈{array}{c}20∖1end{array})×0.680×(1−0.68)20−0+(beg∈{array}{c}20∖1end{array})×0.681×(1−0.68)20−1&amp;nbsp;⇒1.26765×10−10+5.38752×10−9&amp;nbsp;⇒5.51428×10−9&amp;nbsp;Step 2&amp;nbsp;Result:Distribution – Binomial&amp;nbsp;Probability -&amp;nbsp;5.51428×10−9

Sixty-eight percent of adults would still consider a car brand

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