|STAT 13 (1a, 1b, 1c)
Introduction to Statistical Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Friday, Fe. 13, 2004
- Suppose X~ Normal(μ = 23,
σ2 = 4). Use SOCR (http://socr.stat.ucla.edu/) to calculate the following probabilities. Include a snapshot of each
area of interest from your work using the SOCR pages.
- P(X ≤ 19);
- P(X < 19);
- P(24 ≤ X ≤ 27);
- P(20 ≤ X ≤ 27 ∩ 24 ≤ X ≤ 29)
- P(20 ≤ X ≤ 23 ∪ 24 ≤ X ≤ 29)
- The number of liters of soft serve ice cream sold by an ice cream van
driver in an afternoon is found to be Normally distributed with mean
μ = 8.6 liters and standard deviation σ = 1.28 liters. Use the SOCR (http://socr.stat.ucla.edu/) resource to calculate:
- What is the least amount of soft serve ice cream that is needed
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 following problems
where X~Normal(μ = 5.1, σ2 = 0.872 ):
- What is the probability that X is greater than 6?
- What is the probability that X is between 4.3 and 6.6?
- What value of x gives P(X ≤x) = 0.45?
X has a mean of -3 and a standard deviation of 5 and W has a
mean of 5 and a standard deviation of 3. Let X and W be independent
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=3, σ2=16) 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(-2 ≤ X ≤ 0)? Is it different from P(-2 < X < 0)?
(HW_4_3) The height of males is normally distributed with
a mean of 70" (inches) and a standard deviation of 3". Assume also that the
height of women is normally distributed with mean of 65.5" and standard deviation
of 2.5". Calculate and represent graphically the following probabilities.
- What is the chance that a randomly selected male will be 73" to 75" tall?
- If heights of male and female partments are independent (a strong
and unclear assumption) what is the chance that their combined height is
less than 140"?
- Under the above independence assumption, what is the chance that the female is taller than her male partner?
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