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Question 1

Rachel measures the lengths of a random sample of 100 screws. The mean length was 2.6 inches, with a standard deviation of 1.0 inches.

Using the alternative hypothesis (

What is the p-value of the test statistic? Answer choices are rounded to the thousandths place.

Question 2

Song owns a $250,000 house and has a 2% chance of experiencing a fire in any given year. Assume that only one fire per year can occur and that if a fire occurs, the house is completely destroyed. Suppose that Song purchases a full insurance contract from Lemonade Insurance Company for an actuarially fair premium. This contract would pay all losses due to the fire. Assume that Song's contract is the only insurance contract Lemonade Insurance Company sold. a. What is the probability distribution of total losses for Lemonade Insurance Company if they sell a contract to Song? (2 points) b. What is the actuarially fair premium [AFP] Lemonade Insurance Company will charge Song in the coming year? (1 point) What is the amount of risk Lemonade Insurance Company faces if they have Song as their only customer? (2 points)Jack owns a $500,000 house and has a 4% chance of experiencing a fire in any given year. Assume that only one fire per year can occur and that if a fire occurs, the house is completely destroyed. Suppose that Jack purchases a full insurance contract from Lemonade Insurance C. Wmpany for an actuarially fair premium. This contract would pay all losses due to the fire. Assume that Jack's contract is the only insurance contract Lemonade Insurance Company sold. O What is the probability distribution of total losses for Lemonade Insurance Company if they sell a contract to Jack? (1 point) Just now What is the actuarially fair premium [AFP] Lemonade Insurance Company will You charge Jack in the coming year? (1 point) What is the amount of risk Lemonade Insurance Company faces if they have Jack as their only customer? (2 points)Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the standard deviation to be 0.45 oz. The cheese factory lists the package weight at 10 oz. X- U S n The t-statistic for a two-sided test would beA ball is drawn from a bag of 26 red and 12 yellow balls. The process is repeated 50 times, replacing each ball that is drawn. Which of the following statements about the distributions of counts and proportions is TRUE? O The count of drawing a yellow ball is not a binomial distribution, O The count of drawing a red ball is a binomial distribution. O The distribution of the count of drawing a red ball cannot be approximated with a normal distribution. O The distribution of the count of drawing a yellow ball from a sample size of 10 can be approximated with a normal distribution