Answer:
a. Jean, because her commute is in the country.
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score will have the longer commute.
Mary:
Travels for 35 minutes. In big cities, average commutes are 40 minutes with a standard deviation of 15 minutes. This means that
. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{35 - 40}{15}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B35%20-%2040%7D%7B15%7D)
![Z = -0.33](https://tex.z-dn.net/?f=Z%20%3D%20-0.33)
Jean:
Travels for 30 minutes. In rural areas, the average commute is 25 minutes with a standard deviation of 6 minutes. This means that
. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{30 - 25}{6}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B30%20-%2025%7D%7B6%7D)
![Z = 0.83](https://tex.z-dn.net/?f=Z%20%3D%200.83)
Due to being in the Country, Jean's z-score is higher, so her commute is longer. The correct answer is given by option A.
Answer:
m=21
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
We can find the slope if we are given two points
m = (y2-y1)/(x2-x1)
= (4-8)/(4 - -4)
= (4-8)/ (4+4)
= -4/8
= -1/2
In the question, we are given the table of values below.
Using the graph plotter,
The slope(m) and the intercept(c) is given as (nearest tenth)
![m=14.0\text{ and c =}478.7](https://tex.z-dn.net/?f=m%3D14.0%5Ctext%7B%20%20and%20c%20%3D%7D478.7)
This can be inserted into the equation of best fit below
![y=14.0x+478.7](https://tex.z-dn.net/?f=y%3D14.0x%2B478.7)
Also, the correlation coefficient is given as
![r=1.0](https://tex.z-dn.net/?f=r%3D1.0)
The relationship is also strong and positive
The difference between $0.20 and $0.60 is: 0.60 - 0.20 = $0.40
The rate of change in 4 years is $0.40
The rate of change in 1 year is $0.10