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Please answer the attached questions, I will need to know what equations/formulas that were used to arrive at the answer

MATH 146 (Fall 2012) EXAM #3 NAME . ** ANSWERS WITHOUT PROPER JUSTIFICATION WILL NOT BE GIVEN FULL CREDIT ** 1 . Frozen turkeys arrive in a supermarket in groups of 48 (as everyone knows), where there is a 3% rate of return due to spoilage. a) Find the mean number of returned turkeys per group. a)_________________ b) Find the standard deviation for the number of returned turkeys. b)_________________ c) Find the probability of having exactly three returns in a group. c)_________________ 2 . For one particular policy with coverage of $75,000, an insurance company collects a premium of $170. If the insured has a 0.9996 probability of living and a 0.0004 probability of dying, what is the expected value for the insurance company? __________________ 3 . Given that the probability function for x = 1,3,5,7, gives the following probability distribution. Find the mean and standard deviation for the distribution μ =______________ σ =______________ 4 . Given a binomial distribution with n = 28 and p = 0.6, find a) the probability function for the distribution ____________________________ b) P ( 18 ≤ X ≤ 20 ) ______________ 5 . Consider a binomial distribution with n = 64 and p = 0.26. Use the normal distribution to approximate the probability P ( X ≤ 20). ( Note : You must use the normal approximation to get credit)
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________________ 6 . A sample of size 49 is selected from a normal distribution having a mean of 134 and a standard deviation of 14. What is the probability of selecting a sample with a mean exceeding 137? (Hint : CLT) ________________ 7 . Find the following probabilities a) P (-1.34 z 2.17) a)________________ b) P ( z > 1.357) b)________________ 8 . Solve the following for the value of a . P (- a < z < a ) = 0.9488 ________________ 9 . Weights of turkeys are normally distributed with a mean of 12 lbs with a standard deviation of 2.5 lbs, what percent have weights between 12 lbs and 15.1 lbs? ________________ 10 . Scores for the entrance exam at the Crawford School of Statistics are normally distributed with a mean of 624 and a standard deviation of 75. If school’s admissions office (which is . .. me) decides to require scores above the 86th percentile, find the cut-off point for admission.
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