To Projects
IT 223 -- Project 2BC
Part B: Probabilities for Normal Distributions
- Use R to help you solve these problems. Show the R statements that you use
to perform your calculations. Check your answers with the normal tables and
extreme normal tables.
Use the R function pnorm to find the area of the standard
normal curve for the interval (-∞, z]. Use
qnorm to
find the z for which the area of (-∞,
z] is q.
- LSAT scores are normally distributed with mean 150 and SD 10.
What percentage of students taking the LSAT test obtain a score
- under 142?
- over 191?
- between 153 and 174?
- The lengths of horse pregnancies are normally distributed with mean 336 days and
SD 3 days. What percent of the lengths of horse pregnancies are between 335 and 338 days?
- Determine the following percentiles for LSAT scores (see Problem 1 in this
part):
a. 57% b. 98% c. 39%
- Determine these percentiles for horse pregnancies:
a. 89% b. 45%
Part C: Random Number Simulations
- For this section
include the two normal plots in your output, as well as the R statements that
you use to create these plots.
- Perform two simulations with the R functions rnorm and runif to see how normal plots behave.
- Create a data vector consisting of 100 normal random numbers with μ=
5 and σ=3. Use the R function rnorm to
create your dataset.
- Create a normal plot of the normal random numbers in Step 1. Describe this
normal plot using one of these terms: approximately normal, skewed to the left,
skewed to the right, thin tails, fat tails.
- Create a dataset consisting of 100 uniform random numbers, with minimum 2
and maximum 6. Use the R function runif.
- Create a normal plot of the normal uniform random numbers in Step 3.
Describe this normal plot using one of these terms: approximately normal, skewed
to the left, skewed to the right, thin tails, fat tails.