W/4 = –5 what is the value of w?
2 answers:
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Answer:
Step-by-step explanation:
Use the slope-intercept formula: where m is slope and b the y-intercept.
Use the slope formula for when you have two points:
Rise over run is the change in the y-axis over the change in the x-axis. Insert values:
Simplify parentheses (negative+negative=positive)
Simplify
2 is the slope:
Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:
(4,7)
The y-intercept is -1. Insert into the equation. Change the + symbol to -:
Done.
Answer:
There is a 95% chance that values will be within ±2 standard deviations of the mean.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
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.
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this question:
According to the empirical rule, 95% of the measures are within 2 standard deviations of the mean. So the correct statement is:
There is a 95% chance that values will be within ±2 standard deviations of the mean.