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STAT 13 (2a, 2b, 2c)	*Introduction to Statistical Methods for the Life and Health Science*
Department of Statistics	Instructor: Ivo Dinov
Homework 4	Due Date: Friday, Oct. 31, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

The following table of probabilities was obtained from STATA: Normal with mean μ= 8.6 and standard deviation σ= 1.28.

mean

8.6

standard deviation

1.28

(i) What is the least amount of soft serve ice cream that is needed so that the driver can satisfy demand on 90% of afternoons?

Use either SOCR or STATA to solve the following problems where X~Normal(μ = 5.1, σ² = 0.87² ):

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.

(ii) 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:

(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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Instructor: Ivo Dinov