Binomial Pdf Eye Color Name Student Activity Class Follow

binomial pdf eye color name student activity class follow your teachers directions either to create a .tns file or to open the pre-mad

Binomial Pdf Eye Color Name
Student Activity Class
Follow your teacher's directions either to create a .tns file or to
open the pre-made file your teacher sends you (Binomial_Pdf_Eye_Color.tns).
What's the probability of a success? This activity investigates how to
answer that question in a binomial situation.

Several sources indicate that the probability of a person in the
United States having blue eyes is approximately 30%. Suppose you
randomly sampled 50 people in the United States. One basic question to
answer is whether an underlying probability model might describe the
probability of the possible numbers of blue-eyed people in your
sample.
1. This situation involves binomial trials, so the first step is to
check whether the requirements for binomial trials are met: two
outcomes per trial; a fixed number of trials; a constant probability
of success; and independent trials. Verify that these conditions are
met in this context.
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Two outcomes?
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Fixed # of trials?
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Constant probability of success?
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Independent trials?
2. a. Reflect on how you built the .tns file. What two inputs
determined the binomial distribution?
b. For a random sample of 50 people, what would you expect to be the
most likely number of blue-eyed people? Explain your reasoning.
Move to page 1.2.
Press / ¢ and / ¡ to navigate through the lesson.
3. In terms of the context,
a. what does the zero represent in cell A1?
b. what does the value in cell B5 represent?
Move to page 1.3.
If the conditions for binomial trials are met, a binomial model can be
used to represent the probabilities, which is the distribution you
created on Page 1.3.
4. a. Describe the distribution in terms of shape, center, and spread.
b. Describe how the context of the eye color for a sample of randomly
chosen people relates to the graph.
c. Saundra wonders whether the probability of getting 4 blue-eyed
people in the sample of 50 was 0. What would you tell her?
5. Suppose x represents the number of blue-eyed people. Describe how
the graph helps you answer each of the following:
a. What are the most likely outcomes?
b. What are the least likely outcomes?
c. If you add the probabilities of every possible outcome, what should
be the result?
6. a. What is the approximate probability that exactly 10 people will
have blue eyes, P(x=10)?
b. Ten or 11 people will have blue eyes, P(x=10,11)?
c. Fewer than 10 people will have blue eyes, P(x<10)?
d. At least 10 people will have blue eyes, P(x≥ 10)? How could you use
your answer to part b to find the answer to this question?
7. Suppose a researcher was checking the number of candies of a
certain color chosen from randomly selected bags where each bag has
exactly 50 candies. The manufacturer claimed that the probability of
getting a green candy was approximately 0.3.
a. How is this context alike or different from the context involving
eye color above?
b. In a sample size of 50 candy pieces, if the researcher found the
number of green candies in the sample indicated below, should he be
surprised? Explain your reasoning.
i. 12
ii. 8
c. If the researcher were surprised, what conclusions might he draw?
Extension
Follow your teacher's instructions for the following:
Adding the two sliders to the .tns file as described in the Extension
instructions of the Binomial Pdf Eye Color Create document allows you
to change both the sample size and the probability of a success.
8. The probability of having green or light brown eyes with green
specks is about 12%. In a random sample of 100 people, what is the
probability of the following:
a. Finding exactly 6 people with that eye color?
b. Finding at least 16 people with that eye color?
c. Finding anywhere from 7 to 15, including 7 and 15, people with that
eye color?
9. a. Before using the arrows to change anything, predict how your
answers to question 8 might change if the sample size were 30 people.
b. Check your prediction by changing the sample size to 30 and using
the resulting distribution.
10. a. Predict how your answers to question 7 would change if the
sample size remained 100 but the probability of brown eyes was 0.40 or
40%.
b. Check your prediction by changing n and p accordingly and using the
resulting distribution.
11. a. Describe how the distribution changes as the sample size goes
from 100 to 50 people for p=0.4.
b. How would your answer to part a change if the probability of a
success was a different value?
c. Fix the sample size at n=50. Change the values of p, and describe
what happens.
Tech Tip: If you use a large n and a large p, you might need to select
Menu > Window/Zoom > Window Settings… and change the x Max to a larger
value.
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