How do you solve part c 112. T Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve),f(x) = e-ax²a. Graph the Gaussian for a = 0.5, 1, and 2.b. Given thatLe-ar² dx = √==88compute the area under the curves in part (a).c. Complete the square to evaluate∞S8e-(ax²+bx+c) dx, where a > 0, b, and c are real numbers.

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Answered: 112. Gaussians An important function in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 52E

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Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?
(ii)? Let X be a random variable having the gamma distribution with shape parameter α and scale parameter γ,whereα is know and γ is unknown. let Y = σlogX. Show that (i) if σ>0 is unknown, then the distribution of Y is in a location-scale family; (ii) if σ>0 is known, then the distribution of Y is in an exponential family
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=X= IQ of an individual.(a) Find the z-score for an IQ of 106, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 106. (c) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: . Click and drag the arrows to adjust the values. -1.5
1. Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 75 A graph with a bell-shaped curve, divided into 2 regions by a vertical line. The vertical line extends from the bell curve to the x-axis, and is located on the left half, under the curve. The region on the left of this line is shaded. The x-axis below the vertical line is labeled 75. Question content area bottom The area of the shaded region is enter your response here (Round to four decimal places as needed.) 2. Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 83 A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the…
Let X be the TSH level in an individual. It is assumed that X has an exponential distribution with a mean of 3 µIU /mL. A sample of 12 workers from a logging company is taken. If more than half of the individuals in the sample have TSH levels greater than 4.8 µUI /mL, an intervention program is carried out with the total number of workers in the company. How likely is the intervention program to be needed? a) 0,004 b) 0,006 c) 0,086 d) 0,005 e) 0,003
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = X = IQ of an individual. (a) Find the z-score for an IQ of 123, rounded to three decimal places. 1.533 (b) Find the probability that the person has an IQ greater than 123. 0.0630 (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.
1. Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is: (view image)(a) Compute the probability the a certain part will fail in less than 200 weeks.(b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part.(c) Suppose that we select n = 50 parts at random. Approximate the probability that the average lifetime for these 50 parts will be less than 275 weeks?
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=X= IQ of an individual.(a) Find the z-score for an IQ of 90, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 90. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement.
How can I do this problem in excel? The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds. (a) Sketch this exponential probability distribution. A graph with 1 continuous curve is given. The area under the curve is shaded. The horizontal axis is labeled: x and ranges from 0 to 30. The vertical axis is labeled: f(x) and ranges from 0 to 0.15. The curve begins near (0, 0.06) and curves down to the right. It leaves the viewing window near (30, 0.01). A graph with 1 continuous curve is given. The area under the curve is shaded. The horizontal axis is labeled: x and ranges from 0 to 30. The vertical axis is labeled: f(x) and ranges from 0 to 0.15. The curve begins near (0, 0.10) and curves down to the right. It leaves the viewing window near (30, 0). A graph with 1 continuous curve is given. The area under the curve is shaded. The horizontal axis is labeled: x and ranges from 0 to…
(a) Given that X is normally distributed with mean 10 and ?(? > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given: Φ(1) = 0.8413 and Φ(−1/2)=0.3085, where Φ(?) = ?(−∞ < ? < ?)such that ?~?(0,1). (b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter ? = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute?

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