Asked by Quinton Butsch on Jun 09, 2024
Verified
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.What is the probability that a randomly selected tire will have a life of at least 35,000 miles?
A) 0.1587
B) 0.8413
C) 0.0000
D) 1.0000
Normally Distributed
Describes a distribution of data that follows the normal distribution curve, characterized by a bell shape and equal mean, median, and mode.
Life Expectancy
The average period that an organism, especially a human, is expected to live based on demographic factors.
- Comprehend the principles of the standard normal distribution and its uses.
- Understand the importance of the mean and standard deviation within the framework of real-world distributions.
Verified Answer
SL
Saravana LingamJun 13, 2024
Final Answer :
B
Explanation :
We need to find the probability that a randomly selected tire will have a life of at least 35,000 miles. This can be computed as follows:
P(X ≥ 35,000) = P(Z ≥ (35,000 - 40,000)/5,000) [Converting X to a standard normal variable Z]
= P(Z ≥ -1)
= 0.8413 [Using standard normal distribution table]
Therefore, the answer is (B) 0.8413.
P(X ≥ 35,000) = P(Z ≥ (35,000 - 40,000)/5,000) [Converting X to a standard normal variable Z]
= P(Z ≥ -1)
= 0.8413 [Using standard normal distribution table]
Therefore, the answer is (B) 0.8413.
Learning Objectives
- Comprehend the principles of the standard normal distribution and its uses.
- Understand the importance of the mean and standard deviation within the framework of real-world distributions.