[Solved] The random variable x has a normal distribution with μ = 1,000 and σ = 10. Find the probability that x assumes a value more than 2 standard


Question: The random variable x has a normal distribution with \(\mu \) = 1,000 and \(\sigma \) = 10.

  1. Find the probability that x assumes a value more than 2 standard deviations from its mean. More than three standard deviations from \(\mu \) ?
  2. Find the probability that x assumes a value within 1 standard deviations of its mean. Within 2 standard deviations of \(\mu \) ?
  3. Find the value of x that represents the 80 th percentile of this distribution. The 10 th percentile.

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