Answer the following:
- An. Unfair Die Suppose an unfair die is rolled and lt X be the random Variable representing the number Of dots that Would appear With a probability distribution below. Questions: 1 What will be the average number of dots that would appear? 1' ' 2. How does the assumed value of the outcome vmy from the average number of dots that would appear? _ 3. Will _you_ join in a game of Chance using an unfair die? The number of cellular phones sold per day at the E-Cell Retail Store with the corresponding probabilities is shown in the table below. Compute the mean, variance, and standard deviation and interpret the result. Number of cellphones sold per day in a retail store (x) 15 18 19 20 22 Probability (P(x) 0.30 0.20 0.20 0. 15 0.15 Solution: Complete the statement: Ux = [xi . P(x)] = 15(0,30) + 18(0.20) + 19(0.20) + 20(0.15) + 22(0.15) = 98The mean is equal to therefore, it means that the average number of cellular phones of sold per day is To find the variance complete the table below: P(x) x . P(x) x2 . P(x) 4.5 15 0.30 0.20 3.6 18 3.8 19 0.20 3 20 0.15 3.3 22 0.15 82 = [ (x2 . P()] - 12 =__ 0 = V02 = Therefore, the variance of a probability distribution is equal to while the standard deviation is equal to Independent Activity 1 Beth's Bread and Pastry Shop determines the number of cupcakes sold per day with its corresponding probabilities. Find the mean, variance, and standard deviation of the probability distribution below. If Beth, the owner of the shop is claiming that the average number of cupcakes sold in a day is 150 pieces, do you think it is a believable claim? Number of cupcakes sold per day (x) 90 120 135 150 160 175 Probability P(x) 0.15 0.10 0.20 0.20 0.20 0.15 Practice Activity 2 Analyze the following pairs of data and identify which of the following will most likely yield to a higher variance and higher standard deviation. Put a check mark on the appropriate box. 1. Number of students from different grade levels. Number of boys in a family with three children. 2. Number of fish inside the aquarium from different households. Number of fish inside a can from the different local brands of sardines. 3. Number of COVID-19 patients from different hospitals. Number of family members with fever in a barangay. 4. Number of M & M's peanuts inside a 1.69 Oz bag from different retail stores. 99Number of kernels in corn of different sizes. 5. Number of players in a group playing the game "the boat is sinking." Number of passengers in different luxury cruise ships. Independent Activity 2 Give examples of at least two pairs of data that will most likely yield different variance and standard deviation. Identify the one with a higher possible value of variance and explain why
