Question

the gallup organization found that 29% of americans own a cat as a pet. find the probability 6 americans own a cat as a pet. round your answer to 4 decimal places. question help: message instructor

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, $n = 6$, $k = 6$, $p=0.29$, and $1 - p = 0.71$.

Step2: Calculate the combination $C(n,k)$

$C(6,6)=\frac{6!}{6!(6 - 6)!}=\frac{6!}{6!0!}=1$ (since $0!=1$).

Step3: Calculate the probability

$P(X = 6)=C(6,6)\times(0.29)^{6}\times(0.71)^{6 - 6}=1\times(0.29)^{6}\times(0.71)^{0}$. Since any non - zero number to the power of $0$ is $1$, $(0.71)^{0}=1$. Then $P(X = 6)=(0.29)^{6}=0.0005354929\approx0.0005$.

Answer:

$0.0005$