Normal Random Variable - STAT 200 Sections 1-3

Name: Normal Random Variable - STAT 200 Sections 1-3
Brand: Penn State University
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Author: Grace Hughes

This Homework Presentation covers the concept of a normal random variable in statistics and its real-world applications.

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Normal Random Variable
Stat 200 Sections 1-3
Mon Feb 2, 2015
LQ5 available after class
Exam 1 Info is posted
(Can list topics for review Session under

Which as defined is a binomial random variable?
For responses from a random sample of 10 PSU students, the:
A. X = number of textbooks bought at the beginning of the semester - discrete, non-
binomial
B. X = number of students who are on twitter (binomial, how many are on twitter out
of 10) 0 - 10/N)
C. X = student’s blood level of Vitamin D (ng/ml) - continuous
D. X = number of times a student plays a computer game until he or she first wins -
WAITING n?
E. X = time elapsed between when student sits in the classroom and first checks his or
her phone - continuous

3
Conditions: Binomial Distribution
1. n fixed trials
2. Two possible outcomes for each trial (binary data)
Success: what you want
Failure: what you don’t want
3. Outcomes for each trial are independent (partly linked to randomized trials)
4. Probability of success = ( p )
and will remain essentially constant from trial to trial
Note: ideally should replace to meet this condition – but practically do not replace –
in these instances it is okay (when you take a small sample relative to
population size)
Check: if n/N < or equal to .05 it does not matter that you have not replaced
Note: may not always know value of p
5. Variable defined as: X = number of successes with a fixed n
(ideally, the possible values for this random variable are: 0 to n)
Note: original data is categorical

4
Practical Situations:
Form a committee -
no replacement
n N n/N ≤ 0.05 p = 0.5
remains
constant?
indepen-
dent trials
binomial?
1. Four students are
randomly picked from a
class of 10 women and
10 men to serve.
4 20 4/20 = .2
<.05
no no no
2. four students are
randomly picked from a
class of 100 women and
100 men to serve.
4 200 4/200 = .02
< .05
yes yes,
random
yes
3. four students are
randomly picked from a
class of 1000 women
and 1000 men to serve.
4 2000 4/2000 =
0.002
< .05
yes yes,
random
yes
Success = WOMAN
Let X = number of “women among the four selections

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Statistics

Normal Random Variable - STAT 200 Sections 1-3

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