the mean life of a tire is 30,000 km. the standard deviation is 2000 km. 68% of all tires will have a life between _km and _ km
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.34) from the mean for a Z score.
Z = (score-mean)/SD
Insert the values to solve for both +Z and -Z.
To find the range of tire life within which 68% of all tires will fall, we need to first understand the concept of standard deviation and the empirical rule.
The empirical rule states that for a normally distributed dataset:
- Approximately 68% of the values lie within one standard deviation of the mean.
- Approximately 95% of the values lie within two standard deviations of the mean.
- Approximately 99.7% of the values lie within three standard deviations of the mean.
Given that the mean life of a tire is 30,000 km and the standard deviation is 2,000 km, we can use this information to find the range.
First, we calculate one standard deviation:
Lower range = Mean - Standard Deviation
= 30,000 km - 2,000 km
= 28,000 km
Upper range = Mean + Standard Deviation
= 30,000 km + 2,000 km
= 32,000 km
Therefore, approximately 68% of all tires will have a life between 28,000 km and 32,000 km.
To find the range within which 68% of all tires will have a life, we need to consider the standard deviation.
For a normal distribution, approximately 68% of the data falls within one standard deviation from the mean.
Given that the mean life of a tire is 30,000 km and the standard deviation is 2,000 km, we can calculate the ranges as follows:
Lower Range = Mean - (1 * Standard Deviation)
Upper Range = Mean + (1 * Standard Deviation)
Lower Range = 30,000 km - (1 * 2,000 km)
Lower Range = 30,000 km - 2,000 km
Lower Range = 28,000 km
Upper Range = 30,000 km + (1 * 2,000 km)
Upper Range = 30,000 km + 2,000 km
Upper Range = 32,000 km
Therefore, 68% of all tires will have a life between 28,000 km and 32,000 km.