8) Discrete vs. Continuous Variables
If a variable can take on any value between two specified values, it is called a continuous variable; otherwise, it is called a discrete variable.
Some examples will clarify the difference between discrete and continuous variables.
§ Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter’s weight could take on any value between 150 and 250 pounds.
§ Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We could not, for example, get 2.5 heads. Therefore, the number of heads must be a discrete variable.
12) what does the sum equal to? Is it between 0 and 1?
16) the sum would need to be = 1 so add all and subtract from 1
20 a) resource: http://stattrek.com/probability-distributions/discrete-continuous.aspx?Tutorial=Stat c) mean = add all the data in question / number of data values
http://www.purplemath.com/modules/meanmode.htm d) standard deviation: https://www.mathsisfun.com/data/standard-deviation-calculator.html e) P(8) = ?
10) resource: A binomial experiment is a statistical experiment that has the following properties:
§ The experiment consists of n repeated trials.
§ Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
§ The probability of success, denoted by P, is the same on every trial.
§ The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.
36) a. note that there are 4 requirements that can be met – see above resource
b n = 10; p= 0.9; and x = 8 find P(8) = ?
c. the probability data and interpretationd. p(x> = 8) 1 – P(x<8) = ? e. P( 7 <= X <+ 9) = P(7)+P(8)+P(9) = ?
26)What value is in the center? This would be u = ?
standard deviation – The distance to the inflection points is = ? This value would be
36) a) the interpretation for the .3309 value
b) the interpretation for .1107 value
20) Use Table V in the book. The area to the right of the unknown z-score is = ? So, the area to the left is 1 – ?
24) P(x> 65) = 1 – (the value of the area to the left of the z-score).
Find the z-score = x – u /
28) From Table V: Area to the left of z1 = 0.86 = ? and the area to the left of z2 = 2.57 is ? Then take both values and subtract them.
34)From Table V find the area closest to 0.90 = ? What’s the corresponding z-score = ? 90th percentile for X is x = u +z * = ?
Section 7.4 resource for this section: https://www.ltcconline.net/greenl/courses/201/probdist/NormalAreaBinomial.htm
22) a) P(80) = ?
b) P( X ≥ 80) = ? c) P(X<70) = ? d) P( 70 ≤ X ≤ 90) = ?
28) a. P(X ≥ 20) = P(X ≥ 19.5) = ?
b Is part a unusual?