a. Recall that
For , we have
By integrating both sides, we get
If , then
so that
We can shift the index to simplify the sum slightly.
b. The power series for can be obtained simply by multiplying both sides of the series above by .
c. We have
Does anyone know how to solve this
1 answer:
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Answer:
The range of crying times within 68% of the data is (5.9, 8.1).
The range of crying times within 95% of the data is (4.8, 9.2).
The range of crying times within 99.7% of the data is (3.7, 10.3).
Step-by-step explanation:
According to the Empirical Rule in a normal distribution with mean µ and standard deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:
- 68% data falls within 1 standard deviation of the mean. That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.
- 95% data falls within 2 standard deviations of the mean. That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.
- 99.7% data falls within 3 standard deviations of the mean. That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.
The mean and standard deviation are:
µ = 7
σ = 1.1
Compute the range of crying times within 68% of the data as follows:
The range of crying times within 68% of the data is (5.9, 8.1).
Compute the range of crying times within 95% of the data as follows:
The range of crying times within 95% of the data is (4.8, 9.2).
Compute the range of crying times within 99.7% of the data as follows:
The range of crying times within 99.7% of the data is (3.7, 10.3).