Pregunta
Let \( Z \sim N(0,1) \). Accurate to 4 decimal places, evaluate \( P(Z \geq 3.55) \) 0.4998 0.9996 0.0002 0.9998 None of the above.
Ask by Bartlett Li. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( P(Z \geq 3.55) = 0.0002 \)
Solución
1. We are given that \( Z \sim N(0,1) \) and need to compute
\[
P(Z \geq 3.55).
\]
2. Using the cumulative distribution function (CDF) \( \Phi(z) \) for the standard normal distribution, we have:
\[
P(Z \geq 3.55) = 1 - \Phi(3.55).
\]
3. From standard normal distribution tables or using a calculator, we find:
\[
\Phi(3.55) \approx 0.9998.
\]
4. Therefore:
\[
P(Z \geq 3.55) = 1 - 0.9998 = 0.0002.
\]
5. The correct answer is \( 0.0002 \).
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Simplifique esta solución Mind Expander
To find \( P(Z \geq 3.55) \) for a standard normal random variable \( Z \), we can use the standard normal distribution table or a calculator. The value \( P(Z \geq 3.55) \) is equal to \( 1 - P(Z < 3.55) \). Looking at the standard normal distribution table or using a calculator, we find that \( P(Z < 3.55) \approx 0.9998 \). Thus, \[ P(Z \geq 3.55) = 1 - P(Z < 3.55) \approx 1 - 0.9998 = 0.0002. \] So, accurate to four decimal places, we have \[ P(Z \geq 3.55) \approx 0.0002. \] Therefore, the answer is **0.0002**.
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