A boat capsized and sank in a lake Based on an assumption of a mean weight of 148 b, the boat was tated to carry 60 passengers (so the load limit was 8,880 b) After the boat sank, the assumed mean woight for similar boats was changed from 148 b to 173 b Complete parts a and b below. a. Assume that a similar boat is loaded with 60 passengers, and assume that the woights of people are normally distributed with a mean of 178 9 lb and a standard deviation of 40 1 b Find the probability that the boat is overloaded because the 60 passengers have a mean woight greater than 148 lb The probability is (Round to four decimal places as needed) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,941 Ib. Find the probability that the boat is overloaded because the me weight of the passengers is greater than 173 (so that their total weight is greater than the maximum capacity of 2,941 Ib). The probability is (Round to four decimal places as needed.) Do the new ratings appear to be safe when the boat is loaded with 17 passengers? Choose the correct answer below O A. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 17 passengers O B. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe O C. Because 178.9 is greater than 173, the new ratings do not appear to be safe when the boat is loaded with 17 passengers. O D. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 17 passengers.

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.