in a recent report, joes, a memphis - style barbecue chain, states that 13% of its customers order for…

Explanation:

Step1: Identify the binomial - probability formula

The binomial - probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 6$, $p=0.13$, and $1 - p = 0.87$. We want to find $P(X\leq1)=P(X = 0)+P(X = 1)$.

Step2: Calculate $P(X = 0)$

$C(6,0)=\frac{6!}{0!(6 - 0)!}=\frac{6!}{6!}=1$. Then $P(X = 0)=C(6,0)\times(0.13)^{0}\times(0.87)^{6}=1\times1\times(0.87)^{6}\approx0.377149$.

Step3: Calculate $P(X = 1)$

$C(6,1)=\frac{6!}{1!(6 - 1)!}=\frac{6!}{1!5!}=6$. Then $P(X = 1)=C(6,1)\times(0.13)^{1}\times(0.87)^{5}=6\times0.13\times(0.87)^{5}\approx0.396077$.

Step4: Calculate $P(X\leq1)$

$P(X\leq1)=P(X = 0)+P(X = 1)\approx0.377149 + 0.396077=0.773226\approx0.773$.

Answer:

$0.773$