1. Consider the following probability model where X depicts the total number of sunny days in a month that a city may have during the winter and the corresponding probabilities. X 18 19 20 21 22 23 24 25 26 p | 0.25 0.20 0.15 0.10 0.10 0.10 0.05 0.025 0.025 a. What is the expected (mean) number of sunny days? b. What is the standard deviation of the number of sunny days? 2. Let the random variable X represent the prot made on a randomly selected day by a certain store. Assume X follows a Normal distribution, with a mean of $360 and standard deviation $50. a. What is the probability that the prot is between $300 and $400 on a randomly picked day? b. What is the probability that the prot is exactly $300 on a randomly picked day? c. What is the probability that the prot is less than $300 on a randomly picked day? (1. Above what prot level (measured in $) does the top 10% of the prot distribution lie? e. New also consider the random variable Y, which represents the profit made on a randomly selected day by a second store. Assume Y follows a Normal distribution, with a mean of $250 and standard deviation $30. Assume that X and Y are independent. What is the daily expected prot from the two stores?. What is the combined standard deviation from the two stores? 3. A survey was conducted about electronic gadget use amongst college students. 66% of the students said they regularly use a laptop for school work, 12% said they regularly use a tablet for school work, and 3% said they use both. a. What is the proportion of students who regularly use a laptop or a tablet for school work? b. What is proportion of students use neither a laptop nor a tablet for school work