The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of and . Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.
Distribution of proper notation
The value of the theoretical mean is .
The value of standard deviation is
Given in the question that a table with the number of passengers on different charter fishing boats.
The sample mean and the sample standard deviation .
We need to determine the values of and
We have to write the distribution in proper notation, and calculate the theoretical mean and standard deviation.
Let's consider the above table
From the table , the lowest values is and the highest value is .
Therefore, the variable
Hence, the provided data follows the uniform distribution such that
The theoretical mean of the uniform distribution is
Place the value of
The standard deviation of the uniform distribution is
Place the value of
A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. a. Define the random variable. X = _______ b. X ~ _______ c. Graph the probability distribution. d. f(x) = _______ e. μ = _______ f. σ = _______ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probabilit
Suppose that the value of a stock varies each day from with a uniform distribution.
a. Find the probability that the value of the stock is more than .
b. Find the probability that the value of the stock is between role="math" localid="1648188993020" .
c. Find the upper quartile - of all days the stock is above what value? Draw the graph.
d. Given that the stock is greater than , find the probability that the stock is more than .
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