Central Limit Theorem 2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating that the maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult male passengers, since they tend to be heavier than women or children. Assume adult male weights are normally distributed with a mean of 188.6 lb. and standard deviation of 38.9 lb. a.) If 12 men weighed exactly 2004 lb., what would be the average weight? b.) Find the probability that a single man will have a weight greater than your result from part (a). c.) Find the probability that 12 randomly selected men will have a weight greater than your results from part (a). d.) Does the gondola appear to have the correct weight limit? Why or why not?
Central Limit Theorem 2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating that the maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult male passengers, since they tend to be heavier than women or children. Assume adult male weights are normally distributed with a mean of 188.6 lb. and standard deviation of 38.9 lb. a.) If 12 men weighed exactly 2004 lb., what would be the average weight? b.) Find the probability that a single man will have a weight greater than your result from part (a). c.) Find the probability that 12 randomly selected men will have a weight greater than your results from part (a). d.) Does the gondola appear to have the correct weight limit? Why or why not?
Central Limit Theorem 2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating that the maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult male passengers, since they tend to be heavier than women or children. Assume adult male weights are normally distributed with a mean of 188.6 lb. and standard deviation of 38.9 lb. a.) If 12 men weighed exactly 2004 lb., what would be the average weight? b.) Find the probability that a single man will have a weight greater than your result from part (a). c.) Find the probability that 12 randomly selected men will have a weight greater than your results from part (a). d.) Does the gondola appear to have the correct weight limit? Why or why not?
2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating that the maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult male passengers, since they tend to be heavier than women or children. Assume adult male weights are normally distributed with a mean of 188.6 lb. and standard deviation of 38.9 lb. a.) If 12 men weighed exactly 2004 lb., what would be the average weight? b.) Find the probability that a single man will have a weight greater than your result from part (a). c.) Find the probability that 12 randomly selected men will have a weight greater than your results from part (a). d.) Does the gondola appear to have the correct weight limit? Why or why not?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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