Problem 2: Let X be a random variable that represents the flow, in cm³/s that goes through awater pipe that discharges into Lake Ontario at any point in time. You have determined that Xfollows a normal distribution with mean 30cm³/s and standard deviation 5cm³/s.a) What is the probability that the flow through the pipe exceeds 37cm³/s?b) What is the probability that the flow through the pipe is at most 25cm³/s?c) The probability that the flow through the pipe is between 30 - f cm³/s and 30 +f cm³/s is 0.6, what is the value of f?

Given Information: X is a random variable that denotes the flow in cm3/s that goes through a water…

Answered: Problem 2: Let X be a random variable…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The distribution of life spans is approximately normal and u=40, how large a sample is required in order that the probability of committing a type II error be 0.1 when the true mean is 35.9 months? Assume that o = 5.8 months.
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?
The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of µ = 42 and a standard deviation of o = 6. An angler catches an eel from a river. Let: X = the length (in cm) of an eel a) If the normal length of eels is between 30 cm and 45 cm, what percentage of eels fall within this normal range? Round your answer to 2 decimal places. b) What is the probability that an eel is at least 51 cmin length? Round your answer to 4 decimal places. c) The middle 50% of the lengths (in cm) of the eels are between and Round your answers to 2 decimal places d) Due to the symmetry of the normal distribution we know that DIV 20 - DIV -
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assume that X is normally distributed with a mean 150 and standard deviation of 40. find the probability that (A) x is less then 145 and (B) x is grater then 170
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Use this information about the overhead reach distances of adult females: µ = 205.5 cm, σ = 8.6 cm, and overhead reach distances are normally distributed (based on data from th Federal Aviation Administration) If 40 adult females are randomly selected, find the probability that they have a mean overhead reach between 204.0 cm and 206.0 cm.
assume that X is normally distributed with a mean 150 and standard deviation of 40. find the probability that (A) x is less then 158 and (B) x is grater then 178
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
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