9) Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on along train. The automatic hopper car loader is set to put 80 tons of coal in each car. The actualweights of coal loaded into each car are normally distributed, with mean μ = 80 tons andstandard deviation a = 1.5 ton.a) What is the probability that a car chosen at random will have less than 79.0 tons of coal?^b) What is the probability that 20 cars chosen at random will have a mean load weight x of lessthan 79.0 tons of coal?

Mean=80Standard Deviation =1.5Then,X~Normal(mean,Standard deviation)Concept:Z is known as standard…

Answered: 9) Coal is carried from a mine in West…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. (See Handout 1, Example 1). The life expectancy of a particular brand of lightbulb is normally distributed with a mean of 1500 hours and a standard deviation of 75 hours. We want to calculate the probability that a lightbulb will last more than 1440 hours. a) Calculate the critical z-score. b) Label the axis and shade the area under the curve that we are interested in. Hours z-score c) What is the probability that a lightbulb will last more than 1440 hours? d) What is the probability that a lightbulb will last less than 1440 hours?
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9
Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete part a through c a) If 1 adult female is randomly selected. Find the probability that her pulse rate is less than 82 beats per minute (Round to four decimal places as needed) b) If 4 adult females are randomly selected, find the probability that they have a pulse rates with a mean less than 82 beats per minute (Round to four decimal places as needed) c) Why can the normal distribution be used in part (b) even though the sample size don't exceed 30?(options are the image below)
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of 36 and a standard deviation of 10. Suppose that one individual is chosen at random. Find the following (round to 4 decimal places) a) Find the probability that the percent of fat calories a person consumes is more than 40. b) Find the probability that the percent of fat calories a person consumes is less than 35. c) Find the maximum number for the lower quartile of percent of fat calories. d) The middle 70% of the percent of fat calories are from 4 to
The ages of the winners of a cycling tournament are aproximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.5 years. The winner in one recent year was 34 years old. a) Gransform the age to a z-score b) Interpret the results c) Determne whether the age is unusual. ---------------------------------------------------------- a) transform the age to a z-score z=_____ type an integer or decimal rounded to two decimal places as needed
5. The distribution of male weight in the United States has a standard deviation of roughly o = 25 lbs. The average weight u varies from state to state. Suppose you randomly select 100 males in Louisiana and ask their weights, and you compute the average weight Xn of the n = 100 males. a) Assuming that the standard deviation of weight in Louisiana is 25 lbs, what does the Central Limit Theorem tell you the (approximate) distribution of X will be?
Assume that females have pulse rates that are normally distributed with a mean of μ = 73.0 bpm and a standard deviation of σ = 12.5 beats per minute. A) If one adult female is randomly selected find the probability that her pulse rate is less than 80 bpm. B) if 25 adult females are randomly selected find the probability that they have pulse rates with a mean less than 80 bpm
3. Let the weights of 1 kg tea boxes filled with an automatic machine have a normal distribution with a mean of µ=1.03 and a standard deviation of o=0.02 kg. a) What is the probability that any tea box will weigh less than 1 kg? b) What is the probability that any tea box will weigh higher than 1,06 kg?
Assume that the helium porosity (in percentage) of coal sample taken from any particular sean is normally distributed with a true standard deviation of 0.77 how large a sample size is necessary if the width of the 95% internal is to by 0.348 A) 75 B) 76 C) 80 D) 79
Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0μ=74.0 beats per minute and a standard deviation of sigma equals 12.5σ=12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 7777 beats per minute.
A certain office has 4 entrances A, B, C, and D. If three persons come to the office. What is the probability that both pass thru the same entrance.

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