Which are correct statements regarding proofs? Check all that apply. In a paragraph proof, statements and their justifications a

Answer:

Let’s outline the sets:

Integers: The collection of all whole numbers.

Rational: Numbers that can be expressed as the ratio of two integers.

Natural: The collection of positive integers.

Whole numbers: All the values obtainable by repeatedly adding (or subtracting) 1 to a number.

Thus:

2 qualifies as a:

Whole number, because 1 + 1 = 2 (therefore, it’s also an integer).

We can express 2 as 4/2.

As 2 is the fraction of two integers, it is also considered rational.

Since 2 is positive and an integer, it falls into the category of natural numbers.

Therefore, the number 2 exemplifies all four sets.

If we include a negative example, we can consider -3.

-3 is classified as an integer, is not a whole number, and with 9/-3 = -3, thus it is also a rational number.

Now, addressing the questions:

a) Although a single example can be used across all four sets, I have chosen 2 in this instance.

b) Similarly, I demonstrated that 2, as a positive integer, belongs to all four sets, thus:

Positive integers belong to:

The set of integers.

The set of natural numbers.

The set of rational numbers.

The set of whole numbers.

Answer:

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Step-by-step explanation:

Prior concepts

A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".

The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".

Let X denote the random variable of interest, and we identify its distribution:

Also, let signify the sample mean, whose distribution is:

In this case,

Solution to the problem

We seek this probability

Applying the Z-score formula to the probability results in:

To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Answer:

0.047

Detailed breakdown:

Using a Poisson distribution with a mean m, for an area of 0.5 square meters = 1.5

The formula to determine the probability is given by

P[k] = (e^-m * m^k) k!

Thus, we can calculate

P[4] = [(e^-1.5) * (1.5^4)] ÷ 4 * 3 * 2 * 1

= (0.2231301601 * 5.0625) ÷ 24

= (1.12944375) ÷ 24

≈ 0.04706

≈ 0.047

Therefore, the final result is 0.047