In the context of a normal distribution with a mean (μ) of 1124 and a standard deviation (σ) of 60, the 68th percentile is a measure that indicates the weight below which 68% of the data falls.
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the 68th percentile corresponds to a z-score of approximately ±1.
To find the weight at the 68th percentile, we can use the formula:
Weight = μ + z × σ
Substituting the values, we get:
Weight = 1124 + 1 × 60
Weight = 1184
Therefore, the weight representing the 68th percentile is 1184 pounds. This means that approximately 68% of the steers have a weight of 1184 pounds or less, according to the given normal distribution model.
Complete question:
Use the Normal model N("1124,60") for the weights of steers. What weight represents the 68th percentile?