A study conducted by a research group in a recent year reported that 57% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. Round the answers to at least four decimal places. What is the probability that five or more of them used their phones for guidance on purchasing decisions?

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Gennenzip · Accepted Answer

Step 1 The binomial probability distribution is, P(X=x)=(nx)(p)x(1−p)n−x In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success. Let X be the number of cell phone owners used their phones for guidance on purchasing decisions which follows binomial with sample size 15 and probability of success 0.57. Step 2 The probability that five or more of them used their phones for guidance on purchasing decisions is, P(X≥5)=1−P(X&amp;lt;5) =1−[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)] =1−[(150)(0.57)0(1−0.57)15−0+(151)(0.57)1(1−0.57)15−1+(152)(0.57)2(1−0.57)15−2+(153)(0.57)3(1−0.57)15−3+(154)(0.57)4(1−0.57)15−4] =1−(0+0.0001+0.0006+0.0034+0.0134) =1−0.0175 =0.9825 Thus, the probability that five or more of them used their phones for guidance on purchasing decisions is 0.9825.

A study conducted by a research group in a recent year reported that 57% of cell

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