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MAT 470, Worksheet 6 Name:_____________________ 1. Consider a binomial experiment consisting of 100 trials. The probability of success on each problem is 0.15. A portion of the corresponding histogram is shown. Let X be the number of successes. a). What is the mean and standard deviation for this distribution? b). Determine the following binomial probabilities. i). P( X = 10 successes ) = ii). P( X = 15 successes ) = c). Use the normal distribution to approximate the following binomial probabilities i). P( X < 20 successes) = compare with binomcdf(100,0.15,20) = 0.93368 ii). P( X > 18 successes ) = compare with 1 - binomcdf(100,0.15,18) = 0.16283 iii). P( 8 < X < 22 successes) = 2. Let X be a normally distributed random variable with mean 60. Given that P( X < 70) = 0.94, determine the following probabilities: a). P( X > 70 ) = b). P( 60 < X < 70 ) = c). P( X < 60 ) = d). P( 50 < X < 70 ) = 3. For a binomial experiment with 200 trials and probability of success p = 0.6, determine the following values. a). the mean and the standard deviation: = ________, = _________ b). Using the normal distribution, approximate the probability P( 115 < X < 125 ). c). Using the normal distribution, approximate the probability P( 110 < X < 130 ). d). Using the normal distribution, approximate the probability P( X < 130 ). Note binomcdf(200,0.6,130) = 0.9360974 is the actual cumulative probability.