Tell her to set it to 10 minutes

Tell her that with exponential distribution she cannot find such a number because exponential distribution is a discrete distribution.

Tell her that with exponential distribution she cannot find such a number for time slot length because exponential distribution has a uncountable set of possible values (infinitely many possible values).

Tell her to set it at 30 minutes

Determine the mean and standard deviation of . To get the time slot length needed, add standard deviation to the mean. Voilà!

Advise her to find the 95%-quantile using the exponential distribution.

Random variable that can take any value in some part of the real line (in an uncountable set)

is a normally distributed random variable

A continuous random variable can be transformed into a discrete random variable

If you know the probability density function (PDF) of a continuous random variable, then you can find the cumulative distibution function (CDF) by taking a derivative of the PDF.

Random variable with a finite number of possible values always has a finite expected value (i.e. )

Random variable with infinite countable set of possible values always has a finite expected value (i.e. )

Probability that among 5 randomly chosen people no-one is left-handed, is less than 0.5

Probability that among 3 randomly chosen people there is exactly 1 who is left-handed, is 0.243.

Probability that among 5 randomly chosen people at least one is left-handed, is less than 0.5

The number of left-handed people in a group of 20, is approximately normally distributed

Eye color of a randomly selected person

Body weight (kg)

Number of caries-affected teeth (of a dentist's patient)

Cups of coffee consumed yesterday

Net monthly salary (in EUR)

describes the distribution of a continuous variable (e.g. body weight in kg). 

is suitable when the variable can only take non-negative values

is suitable for variables that can take both positive and negative values

has to property that expected value and variance are equal, i.e. .

describes the distribution of counts (e.g. the number of traffic accidents in a day).