In a sample of 1000 tires, with a mean of 250 miles per tire....about how many tires will last longer than 300 miles?
Need to know standard deviation (SD).
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for the Z score. Multiply by 1000.
To determine how many tires will last longer than 300 miles, we need to know the standard deviation of the tire mileage. The information provided in the question, however, only gives us the mean mileage of 250 miles per tire.
Without the standard deviation, we are unable to calculate the exact number of tires that will last longer than 300 miles.
To determine the number of tires that will last longer than 300 miles, you need to know the distribution of tire mileage. Specifically, you would need to know the standard deviation or any information about the shape of the distribution.
However, if we assume that the distribution of tire mileage follows a normal distribution, we can use the concept of the standard deviation to estimate the number of tires that will last longer than 300 miles.
To do this, you would need to know the standard deviation of tire mileage. Let's assume the standard deviation is 50 miles.
First, determine the z-score for a tire lasting longer than 300 miles. The z-score represents the number of standard deviations a particular value is from the mean.
z = (X - μ) / σ
Where:
X = Value you want to evaluate (300 miles)
μ = Mean (250 miles)
σ = Standard Deviation (50 miles)
z = (300 - 250) / 50
z = 50 / 50
z = 1
The z-score for 300 miles is 1.
Now, you can use a z-table or calculator to find the proportion of tires that will last longer than 300 miles. For a z-score of 1, the proportion is approximately 0.8413. This means that about 84.13% of the tires will last longer than 300 miles.
To estimate the number of tires, multiply the proportion by the total sample size:
Number of tires = Proportion * Sample size
Number of tires = 0.8413 * 1000
Number of tires ≈ 841
Therefore, approximately 841 tires in the sample of 1000 will last longer than 300 miles, assuming a normal distribution with a mean of 250 miles and a standard deviation of 50 miles.