|STAT 13 (1a, 1b, 1c)
Introduction to Statistical
Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Wednesday, Nov. 10, 2004
- Suppose X~ Normal(μ = 23, σ2 = 4). Use SOCR (http://socr.stat.ucla.edu/) Distribution-Modeler to calculate
the following probabilities. Include a snapshot of each
area of interest from your work using the SOCR pages.
- P(X ≤ 21.5);
- P(X < 21.5);
- P(24 ≤ X ≤ 27);
- P(20 ≤ X ≤ 27 ∩ 23 ≤ X ≤ 29)
- P(20 ≤ X ≤ 23 ∪ 24 ≤ X ≤ 27)
- The number of liters of soft serve ice cream sold by an ice
driver in an afternoon is found to be Normally distributed with mean
μ = 9.1 liters and standard deviation σ = 2.78 liters.
Use the SOCR (http://socr.stat.ucla.edu/)
resource to calculate:
- What is the least amount of soft serve ice cream that is
so that the driver can satisfy demand on 90% of afternoons?
- What is the interquartile range for the ice cream sales.
- Use either SOCR or STATA to solve the
where X~Normal(μ = 4.1, σ2 = 0.82 ):
- What is the probability that X is greater than 5.1?
- What is the probability that X is between 4.3 and 5.6?
- What value of x gives P(X ≤x) = 0.45?
- X has a mean of -2 and a standard deviation of 4.5
mean of 4.5 and a standard deviation of 3.1. Let X and W be
random variables and let Y = 3X - 3W.
- What are the mean and standard deviation of Y?
- What can we say about the shape of the distribution of Y?
(HW_4_2) Suppose that X~ Normal(μ=2.1, σ2=9)
compute the Z-scores
for the following numbers and state how many SD's each of these
numbers is away from μ:
- What is the probability P(-1.2 ≤ X ≤ 0)? Is it different from
< X < 0)?
- (HW_4_3) Suppose the
height of males is normally distributed with
a mean of 71" (inches) and a standard deviation of 2.9". Assume also
height of women is normally distributed with mean of 65.7" and standard
of 2.6". Calculate and represent graphically the following
- What is the chance that a randomly selected male will be 72.1"
to 73.8" tall?
- If heights of male and female partments are independent (a
and unclear assumption) what is the chance that their combined height
less than 137"?
- Under the above independence assumption, what is the chance
that the female is taller than her male partner?