# Discrete vs. Continuous Variables, law homework help

**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) = ?

Section 6.2** 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 interpretation**d. p(x> = 8) 1 – P(x<8) = ? e. P( 7 <= X <+ 9) = P(7)+P(8)+P(9) = ?**

Section 7.1

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

Section 7.2

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?