Question

The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.7% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status.

Construct the probability distribution function (PDF). (Round your probabilities to five decimal places.)

x	P(x)
0
1
2
3
4
5
6
7
8

Answer 1

ANSWER::

Let X = the number that believes that same-sex couples should have the right to legal marital status.

Because of population size is very large, so we can use binomial distribution to find the probabilities.

Here n = 8, and p = 0.717 (71.7%)

Let's do it in TI-84 calculator.

First enter 0, 1, 2, 3, 4, 5, 6, 7, and 8 in L1

For this use STAT>>>EDIT >>>1:Edit...

Then highlight L2

Clcik On 2ND >>>VARS >>>A:binompdf(

trials: 8 ( because n = 8)

p : 0.717

x values : 2ND >>> 1 ( So we get x values : L1)

Then highlight Paste and enter

Look the following image

then we get the output in L2 column

From the above we get

P(X = 0) = 4.11426 E-5 = 0.00004

Press down arrow key to view the other values.

So the result is as follows:

In excel, the formula are as follows

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