day 12

Question 1

…greaterthan5…

Answer 1

X>5. calc is 1−P(X<5)

Question 2

… no more than 3 …

Answer 2

X < 3 or equal to calc is P(X < 3)

Question 3

…atleast7…

Answer 3

X>7 or equal to calc is 1−P(X<6)

Question 4

…fewerthan10…

Answer 4

X<10. calc is P(X<9)

Question 5

…atmost8…

Answer 5

X<8 or qual to clac is P(X<8)

Question 6

A probability model is a mathematical description of a random
phenomenon consisting of two parts:

Answer 6

1. A sample space, S
2. A way of assigning probabilities to events

Question 7

One common application of discrete probability models occurs when

Answer 7

the random phenomenon is a count.

Question 8

• In what context can we model our random phenomenon using a
  binomial distribution?

Answer 8

1. The random phenomenon is counting the number of times a characteristic
   is observed in a fixed number of observations/trials, n.
2. Those n observations are independent.
3. Each observation’s result can be categorized into two possible values, which
   we will call “success” (characteristic of interest is observed) or “failure”.
4. The probability of a success, p, is the same for each of the n observations.
   * It follows that the probability of failure then equals 1 – p for each observation.

Question 9

We say that n and p are

Answer 9

are parameters that define an application of the binomial
distribution to specific random phenomenon.

Question 10

Mean and Standard Deviation
If X has a Binomial(n,p) distribution, then

Answer 10

• 𝜇𝑋 = 𝑛𝑝
• 𝜎𝑋 = 𝑛𝑝(1 − 𝑝)

Question 11

A density curve

Answer 11

a mathematical model giving
a picture of the overall pattern of the data

Question 12

Features of all density curves:

Answer 12

Features of all density curves:
1. Always on or above the horizontal axis (x-axis)
* All y-coordinates of points on the curve are ≥ 0

2. The total area under the curve is 1
3. The area under the
   curve and above
   any range of values
   represents the
   proportion of all
   observations that
   fall in that range.

Question 13

The Normal distribution is used to describe
data that is

Answer 13

unimodal and symmetric, i.e “bell-
shaped”

Question 14

The standardized value is called a

Answer 14

z-score.

Question 15

z-scores follow a Normal distribution with

Answer 15

mean 0 and
standard deviation 1.