The average age of a vehicle registered in the United States is 8 years, or 96 months. If a random vehicle is selected, find the probability that its age is between 98 and 100 months. Assume the standard deviation for the population is 15.
To find the probability that a random vehicle's age is between 98 and 100 months, we need to find the z-scores corresponding to these ages and use them to calculate the area under the standard normal curve between these z-scores.
First, we calculate the z-score for 98 months:
z1 = (98 - 96) / 15 = 0.1333
Next, we calculate the z-score for 100 months:
z2 = (100 - 96) / 15 = 0.2667
We can use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. For this calculation, we'll assume a standard normal distribution table is used.
Using the table, we find the area corresponding to z1 to be approximately 0.5528, and the area corresponding to z2 is approximately 0.6048.
The probability that a random vehicle's age is between 98 and 100 months is the difference between these two areas:
P(98 ≤ x ≤ 100) = 0.6048 - 0.5528 = 0.052
Therefore, the probability that a random vehicle's age is between 98 and 100 months is approximately 0.052 or 5.2%.