21. A bottling company produces bottles of fruit juice that are filled, on average, with 32 ounces (oz) of juice. Due to random fluctuations in the machinery, the actual volume of juice is normally distributed with a standard deviation of 0.4 ounce. Let P be the probability of a bottle having less than 31 ounces. Express P as an integral of an appropriate density function and compute its value numerically.

21. A bottling company produces bottles of fruit juice that are filled, on average, with 32 ounces (oz) of juice. Due to random fluctuations in the machinery, the actual volume of juice is normally distributed with a standard deviation of 0.4 ounce. Let P be the probability of a bottle having less than 31 ounces. Express P as an integral of an appropriate density function and compute its value numerically.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 29CR

See similar textbooks

Similar questions

Explain the difference between the average rate of change of y as x changes a to b, and the instantaneous rate of change of y at x=a
he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.
A particular professor never dismisses class early. Let x denote the amount of time past the class end time (in minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density curve has two horizontal solid line segments are graphed on the coordinate plane. The horizontal x axis is labeled "Time (minutes)" and has two tick marks labeled "0" and "10". The vertical axis is labeled "Density" and has one tick mark labeled "1/10." The first line segment enters the viewing window from the left and is drawn directly on the negative horizontal axis, ending at (0, 0). The second line segment begins at the coordinate (0, 1/10) and ends at the coordinate (10, 1/10). (a) What is the probability that at most 7 minutes elapse before dismissal? (b) What is the probability that between 3 and 5 minutes elapse before dismissal?
An insurer's annual weather related loss, X, is a random variable with density function f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise. Calculate the 30th percentiles of X. (Round to 2 decimals).
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.
Let X be a random variable that represents the number of processes currently running in your computer, between 50 and 200 processes. Let Y be a random variable that represents your computer's internal temperature between 20 and 100 celcius. Compute the correlation between these two random variables if we model this situation with the joint density function, where K is a scaling constant. To show your work set up all your intervals correctly.
Integration by parts is required. The probability density function for the diameter of a drilled hole in millimeters is 10e1o-4.0) for x> 4.0 mm. Although the target diameter is 4.0 millimeters, vibrations, tool wear, and other nuisances produce diameters larger than 4.0 millimeters. a) Determine the mean and variance of the diameter of the holes. Mean = millimeters (Round your answer to 1 decimal place.) Variance - b) Determine the probability that a diameter exceeds 4.1 millimeters. (Round your answer to 3 decimal places.) millimeters? (Round your answer to 2 decimal places.)
A continuous random variable X has a normal distribution with mean 12. The probability that X takes a value less than 8 is 0.24. Use this information and the symmetry of the density function to find the probability that X takes a value greater than 16.
3. The total claim amount for a health insurance policy follows a distribution with density function f(x)= 1500e-/1500 for x > 0. The insurance has a deductible of $200. Find the mean and the standard deviation of the amount the insurance pays per claim.
Let X be the duration, in minutes, of a long-distance telephone conversation. The density of X is given by:f(x) = (1/10) e^- x/10 x > 0. a) Calculate the average duration of such a call. b) Calculate the variance and standard deviation of X.
A particular professor never dismisses class early. Let x denote the amount of time past the class end time (in minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density curve is shown in the following figure. Two horizontal solid line segments are graphed on the coordinate plane. The horizontal x axis is labeled "Time (minutes)" and has two tick marks labeled "0" and "10". The vertical axis is labeled "Density" and has one tick mark labeled "1/10." The first line segment enters the viewing window from the left and is drawn directly on the negative horizontal axis, ending at (0, 0). The second line segment begins at the coordinate (0, 1/10) and ends at the coordinate (10, 1/10). (a) What is the probability that at most 7 minutes elapse before dismissal? (b) What is the probability that between 3 and 5 minutes elapse before dismissal?