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(04.02 MC)  To increase sales, a cell phone store began giving a free month of service on some cell plan purchases. Customers were unaware whether they would receive the free month until after purchase. The store manager claimed that one in eight customers received the free month. Nine customers each buy a cell phone plan. Let X = the number of customers that receive a free month of cell phone service.Part A: Is X a binomial random variable? Explain. (3 points)Part B: What is the mean and standard deviation of X? Provide an interpretation for each value in context. (4 points)Part C: Three of the nine customers receive a free month of service. Is the store’s claim accurate? Compute P(X ≥ 3) and use the result to justify your answer. (3 points) (10 points)

(05.04 MC)  A researcher has conducted a survey using a simple random sample of 225 elementary teachers to create a confidence interval to estimate the proportion of elementary teachers favoring the addition of a soda machine to the cafeteria. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 25 teachers instead of 225 elementary teachers. Which of the following statements best describes how the confidence interval is affected by this change? (3 points)

(06.06 MC)  Fifteen pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown. Which of the following conclusions is appropriate? (3 points)

(04.02 MC)  An individual can win a prize by drawing the highest numbered card out of five cards. After each draw, the card is replaced and the cards are shuffled for another chance. If the prize is not won, the card is again replaced and mixed in with the other cards. If a prize is won, the highest card is replaced and the five cards are shuffled for a new game. If an individual makes seven draws, what is the probability the individual will win a prize exactly two times? (3 points)

(04.03 MC)  The probability that Babe Ruth hits a home run on any given at-bat is 0.12, and each at-bat is independent. Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points) Part B: What is the expected number of at-bats until the next home run? (5 points) (10 points)

You are seeing a 9-year-old male for a well child exam and as you consider positive parenting approaches, related to gun safety, (evidence posted by peer) you know the following to be true:

(05.02 MC)  The amount people who pay for electric service varies quite a bit, but the mean monthly fee is $168 and the standard deviation is $34. The distribution is not Normal. Many people pay about $90 in rural areas of the country and about $150 in urban areas of the country, but some pay much more. A sample survey is designed to ask a simple random sample of 1,200 people how much they pay for electric services. Let x̄ be the mean amount paid. Part A: What are the mean and standard deviation of the sample distribution of x̄? Show your work and justify your reasoning. (4 points) Part B: What is the shape of the sampling distribution of x̄? Justify your answer. (2 points) Part C: What is the probability that the average electric service paid by the sample of electric service customers will exceed $170? Show your work. (4 points) (10 points)

Please select ALL the following that are true as it pertains to macronutrients

(04.02 MC)  An individual can win a bouncy ball by guessing under which one of four cups the ball is located. After each guess, if the ball is won, a new ball is placed randomly under one of the four cups. If the ball is not won, then the ball is again placed randomly under one of the four cups. If an individual makes five guesses, what is the probability the individual will win a prize exactly two times? (3 points)

Find the polynomial  of degree 3 with integer coefficients, and zeros . ​