Question

Asked Oct 7, 2019

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A random number generator picks a number from 14 to 73 in a uniform manner. Round answers to 4 decimal places when possible.

- The mean of this distribution is
- The standard deviation is
- The probability that the number will be exactly 50 is P(x = 50) =
- The probability that the number will be between 27 and 40 is P(27 < x < 40) =
- The probability that the number will be larger than 40 is P(x > 40) =
- P(x > 15 | x < 29) =
- Find the 42nd percentile.
- Find the minimum for the upper quartile.

Step 1

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Step 2

**Introduction:**

Denote *X* as a number selected by the random number generator.

According to the description of the problem, it can be understood that the random number generator chooses the numbers discretely, such as, 14, 15, 16, …, 72, 73, and does not choose numbers such as 14.25, 17.9, etc.

Thus, *X* follows a discrete uniform distribution between 14 and 73.

*Discrete uniform distribution:*

Suppose a random variable, *X* is defined over the range [*a*, *b*], such that, *X* can take *N* possible distinct, equidistant values...

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