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A homeowner is interested in the average cost of all bathroom remodels. The homeowner has seen that the average cost is $10,750. The homeowner believes that the average cost of a bathroom model is more than this value. They randomly select 41 bathroom remodel costs, and they find that the average cost was $10,900 with a standard deviation of $450. Use a 5% level of significance to test the homeowner’s belief.   State the hypotheses:

Suppose a group of 3 friends are at a dinner party. There are 2 food options they can choose from – meat (M) or vegetarian (V). Choose the sample space for the possible food selections from this friend group. Sample space = [a]

Mia is considering what ice cream flavor to have for dessert. She has a 67% change of picking chocolate, a 32% chance of picking vanilla, and a 27% chance of picking both flavors.   Given that Mia chooses vanilla, what is the probability that she chooses chocolate? [c] (Round to 3 decimals)

Assume that whether it rains today or tomorrow is independent of each other. The probability that it rains today is 0.32 and the probability that it rains tomorrow is 0.87. (Round to 3 decimal places)   a. What is the probability that it rains today and tomorrow? [a] b. What is the probability that it rains at least one of the days? [b]

Luna is ordering at Taco Bell. There is a 42% chance she will order a Crunchwrap, a 63% chance she will order a Chalupa, and a 27% chance she will order both a Crunchwrap and a Chalupa. (Give your answers in decimal form to represent probabilities).   a. What is the probability that Luna orders a Crunchwrap or a Chalupa? [a] b. What is the probability that Luna orders a Crunchwrap but does not order a Chalupa? [b]

A chef is in search of an elusive ingredient he needs for a recipe. He is going to check 2 stores for the ingredient, regardless if he finds the ingredient at the first store. The probability that he will find the ingredient at the first store is 0.21, the probability that he finds it at the second store is 0.15, and the probability that he finds it at both stores is 0.08.    Given the chef finds the ingredient in the second store, what is the probability that he finds it in the first store? [c] (Round to 3 decimals)

Consider the following discrete probability distribution. x P(X = x) 10 0.35 20 0.10 30 0.15 40 0.40 a. Find the probability that X is greater than 20. [a] b. Find the probability that X is less than 40. [b] c. Find the expected value, µ, of X. [c]

A histogram of a set of data indicates that the distribution of the data is left skewed. Which measure of central tendency will be larger, the mean or the ​median?

Data are drawn from a bell-shaped distribution with a mean of 80 and a standard deviation of 2. a. Approximately what percentage of the observations are between 82 and 86? [a] b. Approximately what percentage of the observations are less than 78? [b]

Given the following sample data, answer the following questions: 21  56  58  61  66  67  70   a. Calculate Q1 [a] b. Calculate Q3 [b] c. Calculate the IQR [c] d. Calculate the lower fence [d] e. Calculate the upper fence [e] f. List any outliers (leave blank if no outliers; if there are multiple, separate them with commas) [f]