Use point-slope form − 1 = ( − 1) to find the equation of the line that passes through the point (−3,5) and has slope = −2 . Wri
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Answer:
The mean absolute deviation of this data is
.
Step-by-step explanation:
The mean absolute deviation (MAD) of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
The steps to find the MAD include:
- find the mean (average)
- find the difference between each data value and the mean
- take the absolute value of each difference
- find the mean (average) of these differences
To find the mean absolute deviation of this data you must
Step 1: Calculate the mean.
Step 2: Calculate the distance between each data point and the mean and take the absolute value of each difference .
Step 3: Add the distances together.
Step 4: Divide the sum by the number of data points.
Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have:
Mean , standard deviation
.
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.