A gallon of water weighs 8 1/3 lb. How much does 1 1/5 gallon of water weigh?
2 answers:
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The variance of a distribution is the square of the standard deviation
The variance of the data is 2.2
<h3>How to calculate the variance</h3>Start by calculating the expected value using:
So, we have:
This gives
Next, calculate E(x^2) using:
So, we have:
The variance is then calculated as:
So, we have:
Approximate
Hence, the variance of the data is 2.2
Read more about variance at:
Answer:
The percent of students who scored below 62 is 2.3%.
Step-by-step explanation:
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is used to represent that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.
Then,
- P (-1 < Z < 1) ≈ 0.6827
- P (-2 < Z < 2) ≈ 0.9545
- P (3 < Z < 3) ≈ 0.9973
Given:
μ = 78
σ = 8
<em>X</em> = 62
Compute the distance between the value of <em>X</em> and <em>μ</em> as follows:
Use the relation P (-2 < Z < 2) ≈ 0.9545 to compute the value of P (Z < -2) as follows:
The percentage is, 0.02275 × 100 = 2.275% ≈ 2.3%
Thus, the percent of students who scored below 62 is 2.3%.