Lowe Lambert
09/13/2024 · High School
The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 7.8 cm . a. Find the probability that an individual distance is greater than 207.50 cm . b. Find the probability that the mean for 25 randomly selected distances is greater than 196.20 cm . c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ?
UpStudy ThothAI Solution
Tutor-Verified Answer
Quick Answer
a. The probability that an individual distance is greater than 207.50 cm is approximately 0.0993 or 9.93%.
b. The probability that the mean for 25 randomly selected distances is greater than 196.20 cm is approximately 0.7977 or 79.77%.
c. The normal distribution can be used in part (b) because the population distribution is normally distributed, and the Central Limit Theorem allows us to use the normal distribution for the sample mean, regardless of the sample size.
Step-by-step Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit