Pregunta
\begin{tabular}{l}\( \begin{array}{l}\text { Recent polls suggest that a probability of about } 0.25 \text { of adults } \\ \text { would say they are afraid of heights. Suppose this probability is } \\ \text { true for all adults. Assume responses from different individuals } \\ \text { are independent. }\end{array} \begin{array}{l}\text { 9. What is the probability of having none of } \\ \text { (he } 5 \text { randomly selected adults say that } \\ \text { they are afraid of heights? Round answer } \\ \text { to the nearest thousandths (three decimal } \\ \text { places) }\end{array} \) \\ \( \begin{array}{l}\text { Type a response }\end{array} \) \\ \hline\end{tabular}
Ask by Salazar Parsons. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The probability that none of the 5 randomly selected adults are afraid of heights is 0.237.
Solución
We are given that the probability an adult is afraid of heights is \( p = 0.25 \). Hence, the probability that an adult is not afraid is
\[
1 - p = 1 - 0.25 = 0.75.
\]
For 5 independent adults, the probability that none are afraid is
\[
P(\text{none afraid}) = 0.75^5.
\]
We compute \( 0.75^5 \) step by step:
\[
0.75^2 = 0.75 \times 0.75 = 0.5625,
\]
\[
0.75^3 = 0.5625 \times 0.75 = 0.421875,
\]
\[
0.75^4 = 0.421875 \times 0.75 = 0.31640625,
\]
\[
0.75^5 = 0.31640625 \times 0.75 = 0.2373046875.
\]
Rounded to the nearest thousandth, the probability is
\[
0.237.
\]
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Simplifique esta solución Bonus Knowledge
To find the probability that none of the 5 randomly selected adults say they are afraid of heights, we can use the complement of the probability that an adult is afraid of heights. Since the probability of an adult being afraid of heights is \(0.25\), the probability that an adult is not afraid of heights is \(1 - 0.25 = 0.75\). Now, we need to raise this probability to the power of the number of individuals, due to the independence of their responses: \[ P(\text{none afraid}) = (0.75)^5 \] Calculating it: \[ (0.75)^5 = 0.2373046875 \] Rounding to the nearest thousandths, we get: \[ \text{Probability} \approx 0.237 \]
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