Suppose that the average weight of students in a statistics class is 75.5 kilograms with a standard deviation of 10.3 kilograms.
45% of the students weights are above what kilograms?
To figure out the weight that 45% of the students are above, we need to use the concept of z-scores.
First, we need to convert the given 45% into a decimal by dividing it by 100. So, 45% becomes 0.45.
Next, we need to find the z-score associated with the decimal value of 0.45. We can use a standard normal distribution table or a calculator.
Using a calculator or table, we find that the z-score associated with 0.45 is approximately 0.1257.
Now, we can use the formula for converting a z-score into a raw score, which is:
Raw score = (z-score * standard deviation) + mean
Plugging in the values:
Raw score = (0.1257 * 10.3) + 75.5
Calculating:
Raw score = 1.30291 + 75.5
So, 45% of the students' weights are above approximately 76.803 kilograms.