Question

learning goal from lesson 23.1
i can decide if a model is consistent with results, given a data-
generating process such as simulation.
a spinner has three equal sections, labeled 2, 3, and 4. you spin the spinner twice and find the sum of the two
numbers of spinner lands on. the probability distribution is shown in the histogram below. use the histogram
answer the following 10 - 13.

1. what is the shape of the data distribution shown by the histogram? (1/2 point)

a. normal
b. skewed left
c. skewed right

1. fill in the table for the probability distribution.
2. what is the probability that the sum is not 4? (1 point)
3. what is the probability of getting a sum greater than 5? (1 point)

Explanation:

Question 10

A normal distribution is symmetric. Skewed left has a longer tail on the left, skewed right on the right. The histogram is symmetric around the center (sum = 5).

Step1: List all possible outcomes

When spinning twice, total outcomes \(n(S)=3\times3 = 9\).
Outcomes for sum \(4\): \((2,2)\) → \(n(4) = 1\), probability \(P(4)=\frac{1}{9}\).
Outcomes for sum \(5\): \((2,3),(3,2)\) → \(n(5)=2\), probability \(P(5)=\frac{2}{9}\).
Outcomes for sum \(6\): \((2,4),(3,3),(4,2)\) → \(n(6)=3\), probability \(P(6)=\frac{3}{9}\).
Outcomes for sum \(7\): \((3,4),(4,3)\) → \(n(7)=2\), probability \(P(7)=\frac{2}{9}\).
Outcomes for sum \(8\): \((4,4)\) → \(n(8)=1\), probability \(P(8)=\frac{1}{9}\).

Step1: Use complement rule

\(P(\text{not }4)=1 - P(4)\)
Since \(P(4)=\frac{1}{9}\), then \(P(\text{not }4)=1-\frac{1}{9}=\frac{8}{9}\)

Answer:

A. Normal

Question 11