Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Answer:

a)

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

b)

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

c)

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

Where and

We seek the probability:

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

By applying this formula, we can find the probability:

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

Part b

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

Part c

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

Answer:

According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.

Consequently, a single whole stick of butter will suffice to prepare $100$ cupcakes.