Question

according to a recent survey, 80% of high school students have their own cell phone. suppose you select 10 high school students at random. determine each probability. round your answers to the nearest tenth of a percent if necessary. sample problem p(8 of the students have cell phones) =$_{10}c_{8}cdot(\frac{8}{10})^{8}(\frac{2}{10})^{2}approx45(0.0067)approx0.3015approx30.2%$ p(9 of the students have cell phones) > enter the answer in the space provided. use numbers instead of words. %

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, $n = 10$, $p=0.8$, and $1 - p = 0.2$.

Step2: Calculate the combination $C(n,k)$ for $n = 10$ and $k = 9$

$C(10,9)=\frac{10!}{9!(10 - 9)!}=\frac{10!}{9!1!}=\frac{10\times9!}{9!×1}=10$.

Step3: Calculate $p^{k}$ and $(1 - p)^{n - k}$

$p^{k}=(0.8)^{9}$ and $(1 - p)^{n - k}=(0.2)^{1}$.

Step4: Calculate the probability $P(X = 9)$

$P(X = 9)=C(10,9)\times(0.8)^{9}\times(0.2)^{1}=10\times(0.8)^{9}\times0.2$.
$(0.8)^{9}=0.134217728$, so $10\times0.134217728\times0.2 = 0.268435456\approx26.8\%$.

Answer:

$26.8$