Math Problem Statement
Solution
From the image, you are working on a question that involves calculating probabilities using the standard normal distribution. Let's walk through each part of the question.
You already got parts a, b, and c correct:
- a. is correct.
- b. is correct.
- c. is correct.
However, part d appears to be incorrect. Let's correct it:
d.
To calculate , we need to first find the cumulative probability for using the standard normal distribution table or a calculator.
- The cumulative probability for is approximately 0.9441.
- Since we want , we need to subtract this from 1:
So, the correct answer for part d is:
Would you like any further details on how this was calculated or clarification on the standard normal distribution?
Here are five related questions you might find useful:
- How do you find probabilities for negative -scores in a normal distribution?
- What is the total area under the standard normal curve?
- How do you calculate for different -values?
- How can you use a calculator or statistical software to compute normal probabilities?
- What are some applications of the standard normal distribution in real-world problems?
Tip: Always remember that the total area under the normal distribution curve equals 1, so for , you subtract the cumulative probability from 1.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Standard Normal Distribution
Z-scores
Formulas
Cumulative probability formula for the standard normal distribution: P(z ≤ x)
Complement rule: P(z > x) = 1 - P(z ≤ x)
Theorems
Standard Normal Distribution Properties
Symmetry of the Normal Distribution
Suitable Grade Level
Grades 9-12
Related Recommendation
Standard Normal Distribution: Calculating P(z < -2.31 or z > -1.09)
Find Probabilities for Standard and Non-Standard Normal Distributions
Finding the Area to the Right of x in a Normal Distribution with Complement Rule
Finding the Z-Score for P(Z < z) = 0.9500
Find Z-Scores for Normal Distribution with Shaded Areas of 0.0217