Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

For a standard normal distribution, find:

[tex]\[ P(-2.87 \ \textless \ z \ \textless \ 0.38) \][/tex]

Sagot :

GinnyAnswer
Sure, let's determine the probability [tex]\( P(-2.87 < z < 0.38) \)[/tex] for a standard normal distribution step-by-step.

1. Identify the z-scores:
- The lower z-score is [tex]\( z = -2.87 \)[/tex].
- The upper z-score is [tex]\( z = 0.38 \)[/tex].

2. Determine the cumulative distribution function (CDF) values for the z-scores:
- The CDF gives us the probability that a standard normal random variable is less than or equal to a particular value.
- For [tex]\( z = -2.87 \)[/tex]:
[tex]\[ \Phi(-2.87) \approx 0.002052 \][/tex]
- For [tex]\( z = 0.38 \)[/tex]:
[tex]\[ \Phi(0.38) \approx 0.648027 \][/tex]

3. Calculate the probability that [tex]\( z \)[/tex] is between -2.87 and 0.38:
- This probability is found by subtracting the CDF value at [tex]\( z = -2.87 \)[/tex] from the CDF value at [tex]\( z = 0.38 \)[/tex]:
[tex]\[ P(-2.87 < z < 0.38) = \Phi(0.38) - \Phi(-2.87) \][/tex]
- Substituting the values we have:
[tex]\[ P(-2.87 < z < 0.38) = 0.648027 - 0.002052 \][/tex]
[tex]\[ P(-2.87 < z < 0.38) \approx 0.645975 \][/tex]

Therefore, the probability [tex]\( P(-2.87 < z < 0.38) \)[/tex] in a standard normal distribution is approximately 0.645975.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.