The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either

Answer:

N=27 individuals

Step-by-step explanation:

Analysis of variance (ANOVA) is employed to assess the differences among group means in a sample.

The sum of squares refers to the cumulative square of variation, which is the dispersion between each individual value and the overall mean.

While conducting a multiple regression, we aim to understand the relationship between multiple independent or predictor variables and one dependent or outcome variable.

<passuming we="" have="" src="https://tex.z-dn.net/?f=k" id="TexFormula1" title="k" alt="k" align="absmiddle" class="latex-formula"> independent variables and individuals, we are able to define the corresponding formulas of variation:

We also have this property

The model's degrees of freedom in this instance is determined by where k = 2 represents the number of variables.

For the error's degrees of freedom in this case, it is indicated by . Knowing k allows us to ascertain N.

The total degrees of freedom would be

This leads us to conclude that the correct answer is N=27 participants.

</passuming>

This question is poorly phrased

Complete Question

The lifespans of lions at a specific zoo follow a normal distribution. The average lifespan is 12.5 years with a standard deviation of 2.4 years. Apply the empirical rule (68-95-99.7%) to estimate the likelihood of a lion living between 5.3 and 10.1 years.

Answer:

The likelihood of a lion living from 5.3 to 10.1 years is 0.1585

Step-by-step explanation:

According to the empirical rule:

1) 68% of the data falls within 1 standard deviation of the mean, meaning between μ - σ and μ + σ.

2) 95% of the data is contained within 2 standard deviations around the mean - between μ - 2σ and μ + 2σ.

3) 99.7% of the data lies within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

The mean provided is: 12.5

Standard deviation: 2.4 years

Starting with the first rule:

1) 68% falls within 1 standard deviation from the mean, implying between μ - σ and μ + σ.

μ - σ

12.5 - 2.4

= 10.1

We now apply the second rule:

2) 95% of the data lies within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

Now applying the last rule:

3)99.7% of the data resides within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

The calculations indicate that

5.3 years is at one side of 99.7%

Therefore,

100 - 99.7%/2 = 0.3%/2

= 0.15%

Moreover, 10.1 years corresponds to one side of 68%

Thus

100 - 68%/2 = 32%/2 = 16%

Consequently, the percentage of a lion living between 5.3 to 10.1 years is evaluated as 16% - 0.15%

= 15.85%

Thus, the estimated probability of a lion surviving between 5.3 and 10.1 years

is represented as a decimal =

= 15.85/ 100

= 0.1585

F(2) denotes function 2 f(2)=f(X))

The formula for the box's volume is V = (length)(width)(height). If we denote the side length of the cutouts as x, we establish V = (28 - 2x)(22 - 2x)(x). Explanation: We intend to excise x by x squares from each corner of a 28 by 22-inch poster board, leading to bottom dimensions of 28 - 2x and 22 - 2x, with a height of x. This expression can be left as is or multiplied and simplified if desired. If we select x = 2 (a random choice as you did not specify), the box's volume calculates to V = (28 - 2*2)(22 - 2*2)(2), rendering V = (24)(18)(2) cubic inches. Since x measures length, it must be greater than zero. Furthermore, the base width of the box can't fall below zero, establishing the inequality for x: 22 - 2x > 0, meaning 11 - x > 0, or x < 11. If we check with x = 10, then V = (28 - 20)(22 - 20)(10). Is this greater than zero? YES. Thus, x < 11 is indeed a reasonable domain in this context.