Best solutions to - "Deviation boundary% of data points within boundary Probability..."

Carol Valentine

Answered question

2021-12-06

Deviation boundary% of data points within boundary Probability of any particular data point being outside boundary +20 +36 68.0 95.40 99.70 Csp Tm 8.00M dCi 32.0% 4.60% 0.30%

Answer & Explanation

temzej9

Beginner2021-12-07Added 30 answers

Step 1
The probability that a random variable X lies in the interval is given below:

P (μ - σ < X < μ + σ) = \int_{μ - σ}^{μ + σ} f (x) d x

\pm σ

P (- 1 < z < 1) = \int_{- 1}^{1} f (z) d z

= 2 \times \int_{0}^{1} f (z) d z

2 \times 0.3413

= 0.6886

= 68 %

Step 2
2)

\pm 2 σ

P (- 2 < z < 2) = \int_{- 2}^{2} f (z) d z

= 2 \times \int_{0}^{2} f (z) d z

= 2 \times 0.472

= 0.954

= 95.4 %

\pm 3 σ

P (- 3 < z < 3) = \int_{- 3}^{3} f (z) d z

= 2 \times \int_{0}^{3} f (z) d z

= 2 \times 0.49865

= 0.9973

= 99.7 %

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