The Laughing Butter Company introduced its newest recipe with the following slogan "Few drops of cannabis mixed with butter will guarantee laughter or better." To analyze the effect of the new butter, Happy High, the lead scientist in the company decided to test how long people will stay happy / laugh after consuming a quarter table spoon of the new butter. It is believed that the effect of the butter lasts somewhere between 5 minutes and 42 minutes. Jose volunteered to be part of the experiment. Let L= time of happiness that Jose will have after the first quarter table spoon. Find P(833), P(032), Find the mean and the standard deviation for this uniform probability distribution.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...