STAT 251GOnline className_________________________________ Date___________________1. A couple plans to have 3 children. How many possible outcomes are there? Draw a tree diagram to show the sample space. What is the probability that they will have exactly 2 girls and 1 boy?2. Given eight students, three of which are female, if two students are selected at random, without replacement, what is the probability that both students are female? Explain your reasoning.3. On an eight-question true-false quiz, a student guesses each answer. What is the probability that the student gets at least one of the answers correct? Explain your reasoning.4. A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done? Explain your reasoning.5. The number of cartoons watched on Saturday mornings by students in Mrs. Kelly’s first grade class is shown below.Number of cartoons watched X012345Probability P(X)0.150.200.300.100.200.05Find the mean, variance, and standard deviation. Show the correct formulas and your work.6. Find thezvalue to the right of the mean such that 85% of the total area under the standard normal distribution curve lies to the left of it? Explain how you found your answer..png”>7. The mean weight of loads of rock is 43.0 tons with a standard deviation of 10.0 tons. If 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 41.9 tons. Assume that the variable is normally distributed. Show all work, including your sketch of the normal distribution with the correct area shaded.8. Mrs. Smith’s reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed. Show all work.

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