http://www.ck12.org Chapter 7. Sampling Distributions and Estimations
From the above table and histogram, you now have some estimates with which to work. The′ 4 ′represents ’4 or more’
but there are only 0.058 or 5.8% of the houses that fall in this category. As well, if you add 0. 380 + 0. 142 + 0 .058,
you will see that a little more than 50%( 0. 580 )of the households will have 2 or more cable hook-ups. The above
distribution is skewed toward the larger numbers and has a mean of approximately 1.746. By using probability from
samples with known distributions, you now have some data for the unknown population.
The data above can also be shown in another way to display numbers that represent the possible number of hook-ups
in each household. This display is done by using a list of random digits to select a household at random from this
distribution. The numbers must be three-digit numbers because the percentages all have three decimal places.
TABLE7.6:
Number of Hook-ups per House-
holdProportions of Households Random Numbers Representing
this Category
0 0. 092 001 − 092
1 0. 328 093 − 329
2 0. 380 330 − 382
3 0. 142 383 − 524
4 0. 058 525 − 582A three-digit random number does not represent an individual household, but with other three-digit numbers in its
category, it represents the many households in the category.
From this display, you can see that 92 households out of 1000 require no cable hook-up while 328 out of 1000
require one cable hook-up. This way of displaying the data allows you to see actual numbers for each household.
Probability distribution is the set of values that a random variable takes on. Its value depends upon the result of
a trial. The random variable,X, will represent the number of cable hook-ups in a randomly selected household.
Therefore,P(x= 2 )≈ 0 .380, because approximately 38.0% of the randomly selected households require two cable
hook-ups.