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Griffin Luna
11/15/2023 · High School

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 4 days. Let \( X \) be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? \( \mathrm{X} \sim \mathrm{N}( \) b. If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 21 and 24 days. d. \( 75 \% \) of all of these types of trials are completed within how many days? (Please enter a whole number)

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a. \( X \sim N(22, 16) \) b. The probability that a trial lasted at least 24 days is approximately 0.3085. c. The probability that a trial lasted between 21 and 24 days is approximately 0.2902. d. 75% of trials are completed within approximately 25 days.

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