Passengers died when a particular water taxi sank. Men are typically heavier than women and​ children, so when loading a water​ taxi, assume a​ worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 196 lb and a standard deviation of 41lb. The water taxi that sank had a stated capacity of 25 ​passengers, and the boat was rated for a load limit of 3750lb. Complete parts​ (a) through​ (d) below   a. the max mean weight is________________lb   b.  if the water is filled with 25 randomly selected men, what is the  probability that thier mean weight exceeds the vlue from part (a)?   c.  after the water taxi sank, the weight assumptionswere revised so that the new capacity became 20 passengers. if the water taxi is filled wiwth 20 randomly seleed men, what is the probability tht their mean weight exceeds 187.5 lb, which is the max mean weight that does not cause the total load to exceed 3750ld.   d.  is the new caoacity of 20 passenger safe?

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 + ...