Normal Distribution Characteristics
- Use
snorm()
fromNCStats
to answer the following questions. [Hint: Click the gear icon and then use the slider bars to answer the two questions below.]- What happens to the normal distribution if μ is increased?
- What happens to the normal distribution if σ is increased?
- For each situation below, (i) identify μ, (ii) identify σ, and (iii) draw the normal distribution with an approximately accurate scale on the x-axis.
- X~N(75,10)
- Y~N(5500,600)
Hand Calculations
Answer each question below, without using R, assuming that X~N(75,10). Show your work completely, including providing a careful drawing for each question.
- What percent of X values are less than 95?
- What percent of X values are greater than 105?
- What percent of X values are between 65 and 85?
- What percent of X values are between 55 and 85?
- What is the value X such that 2.5% of X values are lower?
- What is the most common 95% of X values?
- What is the largest 2.5% of X values?
Carpenter Ants I
Suppose that the distribution of number of Carpenter Ants (Camponotus spp.) in a nest is known to be N(1400,300). From this, answer the following questions.
- What is an individual?
- What is the variable?
- What type of variable is that?
- What is μ?
- What is σ?
Additionally, identify the type of question (e.g., “forward-left”, “reverse-between”) for each question below (you will answer the question in the next assignment).
- What percentage of nests have more than 1900 ants?
- What is the number of ants such that 15% of nests have more ants?
- What is the number of ants such that 33% of nests have fewer ants?
- What percentage of nests have between 700 and 1900 ants?
- What percentage of nests have fewer than 300 ants?
- What is the number of ants such that 5% of nests have more ants?
- The most common 80% of nests have between what two numbers of ants?