Suppose that the average weight of students in a statistics class is 75.5 kilograms with a standard deviation of 10.3 kilograms.
42% of the students weights are above what kilograms?
To find the weight above which 42% of the students fall, we need to calculate the z-score corresponding to the 42nd percentile and then convert it back to a weight value using the mean and standard deviation of the data.
1. Find the z-score corresponding to the 42nd percentile:
Since we are looking for the weight above which 42% of the students fall, the remaining 58% (100% - 42%) of the students will weigh below this value. We need to find the z-score that corresponds to the 58th percentile, as the standard normal distribution table provides values for percentiles below the mean.
Using a standard normal distribution table, find the z-score that corresponds to the 58th percentile. In this case, it is approximately z = 0.22.
2. Convert the z-score back to a weight value:
Now that we have the z-score, we can use the formula: z = (x - mean) / standard deviation, where x is the weight value we are looking for. Rearranging the formula, we get:
x = (z * standard deviation) + mean
Substituting the values we have, we get:
x = (0.22 * 10.3) + 75.5
x = 2.26 + 75.5
x ≈ 77.76
Therefore, approximately 77.76 kilograms is the weight above which 42% of the students in the statistics class weigh.