http://www.ck12.org Chapter 15. Concepts of Statistics
There is a second programmed feature in the distribution menu that performs this calculation. You are looking for
how many standard deviations above the mean will include 98% of the data.
invNorm(0.98) = 2.0537
A person would have to be greater than about 2 standard deviations above the mean to be in the top 2 percent.
- Normalcdf(-1E99, 26, 10, 6) = 0.9961 or 99.61%
The vast majority of the pumpkins weigh less than the 26 pound pumpkin you found.
Practice
Consider the standard normal distribution for the following questions.
- What is the mean?
- What is the standard deviation?
- What is the percentage of the data below 1?
- What is the percentage of the data below -1?
- What is the percentage of the data above 2?
- What is the percentage of the data between -2 and 2?
- What is the percentage of the data between -0.5 and 1.7?
- What is the probability of a value of 2?
Assume that the mean weight of 1 year old girls in the USA is normally distributed, with a mean of about 9.5
kilograms and a standard deviation of approximately 1.1 kilograms. - What percent of 1 year old girls weigh between 8 and 12 kilograms?
- What percent of girls weigh above 12 kilograms?
- Girls in the bottom 5% by weight need their weight monitored every 2 months. How many standard deviations
below the mean would a girl need to be to have their weight monitored?
Suppose that adult women’s heights are normally distributed with a mean of 65 inches and a standard deviation of 2
inches. - What percent of adult women have heights between 60 inches and 65 inches?
- Use the empirical rule to describe the range of heights for women within one standard deviation of the mean.
- What is the probability that a randomly selected adult woman is more than 64 inches tall?
- What percent of adult women are either less than 60 inches or greater than 72 inches tall?