Sectlon Exerclse 6-4 (Algo)On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, sassigned the following probability distribution to the number of tubes she will rent on a randomly selected day.2550487510026TotalP(x)12141.00(a) Calculate the expected value and standard deviation of this random variable X. (Round your answers to 2 declmal placesExpected valueStandard deviation29.65(b) Describe the shape of this distribution.O Skewed to the rightO Skewed to the leftO Symmetrice here to search近

Expectation of a Discrete Random Variable: The expectation of a discrete random variable X, denoted by E(X), is defined as a measure of central tendency of the probability distribution of X. If X has the values x1, x2, ... with probabilities p1, p2, ... then the expectation of X is given by, Standard Deviation of a Random Variable: The standard deviation of a random variable X is defined as a measure of dispersion of the probability distribution of X. It is given by,Using the given data, we find the expected value and standard deviation of X as: x P(x) x.P(x) x2.P(x) 25 0.12 3 75 50 0.48 24 1200 75 0.14 10.5 787.5 100 0.26 26 2600 Total 1.00 63.5 4662.5 The expectation of X is, The working formula of standard deviation is given by, Now, Therefore, the standard deviation of X is, Answer: The blanks will be filled up with 63.5 and 25.10 respectively.Here, the maximum probability is 0.48 which is near to 0.5. This probability is associated with a value of x which is at the beginning of the probability distribution of x. The tail of the distribution of x is longer in the right side. Therefore, the distribution of rightly skewed. Answer: The correct answer is: First Option. Therefore, all other options are incorrect.