The top-selling Amar tire is rated 70,000 KMs, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 KMs and a standard deviation of 6,400 KMs.
What is the probability that a tire wears out before 70,000 KMs? What is the probability that a tire lasts more than 100,000 KMs?
Note: You may use Z-table for this
You can play around with Z table stuff at
davidmlane.com/hyperstat/z_table.html
To find the probability that a tire wears out before 70,000 KMs, we need to calculate the z-score and then find the corresponding probability from the Z-table.
Step 1: Calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value we are interested in (70,000 KMs), μ is the mean (82,000 KMs), and σ is the standard deviation (6,400 KMs).
z = (70,000 - 82,000) / 6,400
Step 2: Look up the z-score in the Z-table. The z-table provides the probability associated with each z-score.
Looking up the z-score of -1.875 in the Z-table, we find that the corresponding probability is 0.0301.
Therefore, the probability that a tire wears out before 70,000 KMs is approximately 0.0301, or 3.01%.
To find the probability that a tire lasts more than 100,000 KMs, we follow a similar process.
Step 1: Calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value we are interested in (100,000 KMs), μ is the mean (82,000 KMs), and σ is the standard deviation (6,400 KMs).
z = (100,000 - 82,000) / 6,400
Step 2: Look up the z-score in the Z-table to find the probability associated with the z-score.
Looking up the z-score of 2.8125 in the Z-table, we find that the corresponding probability is 0.9956.
Therefore, the probability that a tire lasts more than 100,000 KMs is approximately 0.0044, or 0.44%.