Find the equation of the line through the points (3,-4) and (0,2) answer in slope intercept form
1 answer:
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Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties
Where and
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:
So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:
Answer:
Alex has to cycle times faster.
Step-by-step explanation:
Let x meters per minute be Alex's initial rate. If Alex’s bike ride to work usually takes 22 minutes, then the distance from home to work is 22x meters.
One morning he found a new bike route that was 5 minutes faster, then he spends 22-5=17 minutes on the way home cycling at the rate x meters per minute. Then the length of the new route is 17x meters.
If he decides to use this new route again and wants to reach home by an additional 2 minutes earlier, then he will spend 17-2=15 minutes to cover 17x meters. So, the new rate will be
Now,
so, Alex has to cycle times faster.