Question

In: Statistics and Probability

The percent of persons (ages five and older) in each state who speak a language at...

The percent of persons (ages five and older) in each state who speak a language at home other than English is approximately exponentially distributed with a mean of 13.61.

  1. The lambda of this distribution is
  2. The probability that the percent is larger than 4.36 is P(x ≥ 4.36) =
  3. The probability that the percent is less than 14.22 is P(x ≤ 14.22) =
  4. The probability that the percent is between 10.61 and 14.61 is P(10.61 ≤ x ≤ 14.61) =

Solutions

Expert Solution

Let X be the percent of persons (ages five and older) in each state who speak a language at home other than English.

X is exponentially distributed with mean 13.61.

a) If lambda is the parameter of X, we know that the expected value of X is

ans: the lambda of this distribution is 1/13.61

b) The probability density function (pdf) of X is

The cumulative distribution function of X, or P(X<=x) is

The probability that the percent is larger than 4.36 is

ans: The probability that the percent is larger than 4.36 is 0.7259

c)  The probability that the percent is less than 14.22 is

ans: The probability that the percent is less than 14.22 is 0.6482

d) The probability that the percent is between 10.61 and 14.61 is

ans: The probability that the percent is between 10.61 and 14.61 is 0.1168

orchestra answered 1 year ago
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