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:
Katherine will create at least 8 playlists. Each of these will feature 4 pop songs and 9 rock songs.
Detailed Explanation:
Katherine has a library of 32 pop songs and 72 rock songs on her mp3 player. She intends to distribute these into playlists, ensuring an equal count of pop and rock songs in each.
To determine the minimum number of playlists, we find the GCF of the two numbers provided.
For 32, we can express it as 2^5, and 72 can be described as 2^3*3^2
Thus, the GCF for the two figures is 2^3, equaling 8.
Consequently, she will generate 8 playlists, with each containing 4 pop songs and 9 rock songs.
The following table presents the conversion from degrees to gradients.
To calculate the slope, we take the difference between the two y-values (gradients) and divide it by the difference between the corresponding x-values (degrees).
For this purpose, we will use the initial and final points listed in the table. Therefore, the slope m is calculated as:
After rounding to two decimal places, the slope of the line converting degrees to gradients is 1.11
