Answer:
The probability that a randomly selected x-value lies between μ − 2σ and μ is the shaded area under the normal curve shown. P(μ − 2σ ≤ x ≤ μ) = 0.135 + 0.34 = 0.475
Step-by-step explanation:
Correct Answer is 0.8385
Empirical Rule:
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations from the mean.
Here,
The 68-95-99.7 rule for the normal distribution says:
P(μ - σ ≤ x ≤ μ + σ) = 0.68
P(μ - 2σ ≤ x ≤ μ + 2σ) = 0.95
P(μ - 3σ ≤ x ≤ μ + 3σ) = 0.997
By taking the left half of the first interval and the right half of the last
interval, we have:
P(μ - σ ≤ x ≤ μ + 3σ) = 0.5*P(μ - σ ≤ x ≤ μ + σ) + 0.5*P(μ - 3σ ≤ x ≤ μ + 3σ) =
0.34 + 0.4985 = 0.8385
Learn more about Standard normal distribution here:
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