Final answer:
The 60th percentile of a normal distribution is found by using the invNorm function with the percentile expressed as a decimal (0.60), along with the distribution's mean and standard deviation. The output gives the score below which 60 percent of the data would fall.
Step-by-step explanation:
To find the 60th percentile of a normal distribution, you need to determine the score below which 60 percent of the data falls. The process involves using a statistical function called the inverse of the normal cumulative distribution function, commonly referred to as invNorm. Here's a step-by-step guide to find the 60th percentile:
- Identify the mean (μ) and standard deviation (σ) of the normal distribution.
- Use a statistical calculator or software that has the invNorm function.
- Input the percentile value (0.60) as the area to the left of the desired score, along with the mean and standard deviation values into the invNorm function. For example, invNorm(0.60, mean, standard deviation).
- The output will be the score that corresponds to the 60th percentile.
This is similar to how you would find other percentiles, such as the 70th percentile or 90th percentile, by changing the percentile value in the invNorm function accordingly.
For example, if you had a normal distribution with a mean score of 65 and a standard deviation of 5, the 60th percentile can be found by inputting these values into the invNorm function like so: invNorm(0.60, 65, 5). The output will give you the score at which 60 percent of the data would fall below.