If Z is a standard normal random variable, P(-1 ≤ Z ≤ 1) is approximately which value?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $24.99Unlock all

Enhance your understanding of Descriptive Statistics and Probability. Study with interactive questions and detailed explanations. Prepare effectively for your test!

Multiple Choice

If Z is a standard normal random variable, P(-1 ≤ Z ≤ 1) is approximately which value?

Explanation:
In a standard normal distribution, about 68% of the probability lies within one standard deviation of the mean, that is between -1 and 1. This central area corresponds to roughly 0.6827 of the total probability. You can see this from the standard normal cumulative distribution function: Φ(1) ≈ 0.8413, and by symmetry Φ(-1) ≈ 0.1587, so P(-1 ≤ Z ≤ 1) = Φ(1) − Φ(-1) ≈ 0.8413 − 0.1587 ≈ 0.6826 ≈ 0.6827. Equivalently, it’s twice the area from 0 to 1, about 0.3413, giving 0.6826. Thus the probability is approximately 0.6827.

In a standard normal distribution, about 68% of the probability lies within one standard deviation of the mean, that is between -1 and 1. This central area corresponds to roughly 0.6827 of the total probability. You can see this from the standard normal cumulative distribution function: Φ(1) ≈ 0.8413, and by symmetry Φ(-1) ≈ 0.1587, so P(-1 ≤ Z ≤ 1) = Φ(1) − Φ(-1) ≈ 0.8413 − 0.1587 ≈ 0.6826 ≈ 0.6827. Equivalently, it’s twice the area from 0 to 1, about 0.3413, giving 0.6826. Thus the probability is approximately 0.6827.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy