38.6k views
1 vote
For a standard normal distribution, find: P(z<2.15) Express the probability as a decimal rounded to 4 decimal places.

User Marilyne
by
7.7k points

1 Answer

5 votes

Final Answer:

The probability P(z < 2.15) for a standard normal distribution is approximately 0.9842 when rounded to four decimal places.

Step-by-step explanation:

In a standard normal distribution, the area under the curve to the left of a specific z-value represents the cumulative probability up to that point. Using a z-table or statistical software, we find that the z-score of 2.15 corresponds to an area or probability of approximately 0.9842.

This means that there's a 98.42% probability of observing a value less than 2.15 standard deviations above the mean in a standard normal distribution. Visualizing this on a standard normal curve, the shaded area to the left of the z-score 2.15 represents this probability.

Understanding probabilities in a standard normal distribution is crucial in various fields, especially in statistics, where it helps in making predictions or drawing conclusions about certain events or values based on their likelihood within a standard normal curve.

User Berezh
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories