The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 minutes. 40 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of X~ N(21, 2.6) What is the distribution of ¯x~ N(21,0.4111) What is the distribution of ∑x~ N(840,16.4438) If one randomly selected runner is timed, find the probability that this runner's time will be between 20.8833 and 21.4833 minutes 0.0913 For the 40 runners, find the probability that their average time is between 20.8833 and 21.4833 minutes. 0.4913 Find the probability that the randomly selected 40 person team will have a total time less than 832 For part e) and f), is the assumption of normal necessary No. The top 10% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round minutes

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."

Write and test a python program to find and print the largest number in a set of real (floating point) numbers. the program should first read a single positive integer number from the user, which will be how many numbers to read and search through. after reading in all of the numbers, the largest of the numbers input (not considering the count input) should be printed.

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