To calculate Zara's hopping probabilities, locate the areas under the standard normal curve using a z-table for the given z-scores and subtract as needed to find the probability in the specified range.
The question involves the calculation of probabilities using the standard normal distribution, which means we'll be using z-scores to find the probability that a certain variable falls within a range. To find the probabilities for Zara's hopping distances, we use a z-table.
For the range -1.04 to 1.45, we need to find the area under the curve that lies between these two z-scores. The area to the left of z = 1.45 (you can find this using a z-table or a standard normal distribution calculator) minus the area to the left of z = -1.04 gives us the probability that Zara is in the comfortable enchanted zone.
For the range 1.0 to 3.45, similarly, we find the area to the left of z = 3.45 and subtract the area to the left of z = 1.0, to obtain the probability of Zara feeling adventurous. These probabilities must be between 0 and 1, and the sum of all probabilities in the distribution must equal 1.0, as per the rules of probability.
The exact areas and thus the probabilities can be found using a z-table or statistical software.
The probable question may be:
In a magical land, there is a friendly creature named Zara who loves to hop around the meadow. Zara's hopping distances follow a special pattern, and we've named it Z, the Zara Variable.
(i) What is the probability that Zara's hopping distance falls between -1.04 and 1.45? Imagine this as the enchanted zone where Zara feels perfectly comfortable.
(ii) Now, let's explore the mystical region where Zara is feeling a bit more adventurous. What is the probability that Zara's hopping distance is between 1.0 and 3.45?
Additional Information:
Zara's magical hopping distances are measured in standard deviations from the mean. When Zara is in the range -1.04 to 1.45, it's like she's exploring a cozy section of the meadow where she feels at ease. On the other hand, when Zara hops between 1.0 and 3.45, it's a bit like she's venturing into a more exciting part of the meadow, embracing a magical journey.