(a) A machine fills coke into bottles automatically. Actual volumes are normally distributedwith u = 500 ml and o = 10 ml.(i) Determine the probability that the bottles are filled within the tolerance limit of 485ml to 515 ml.(ii) Suppose the mean remains the same. Determine the change needed in the standarddeviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.(b) It was found that an exponential distribution with a mean of 5 minutes was suitable tomodel the duration of a visitor at a website.(i) Find the probability that the website is viewed for at least 3 minutes.(ii) If the website has already been viewed for 1.5 minutes, find the probability that thehome page is viewed for an additional 0.5 minutes.(c) Jones figures that the total number of thousands of miles that an auto can be driven beforeit would need to be junked is uniformly distributed over [0, 40]. Smith has a used car thathe claims has been driven only 10,000 miles. If Jones purchases the car, determine theprobability that she would get at least 20,000 additional miles out of it.

Hello. Since you have asked multiple questions, we will solve the first question for you. If you…

A machine fills coke into bottles automatically. Actual volumes are normally distributed with µ = 500 ml and o 10 ml. (i) Determine the probability that the bottles are filled within the tolerance limit of 485 ml to 515 ml. (ii) Suppose the mean remains the same. Determine the change needed in the standard deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.

A machine fills coke into bottles automatically. Actual volumes are normally distributed with µ = 500 ml and o 10 ml. (i) Determine the probability that the bottles are filled within the tolerance limit of 485 ml to 515 ml. (ii) Suppose the mean remains the same. Determine the change needed in the standard deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.

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...

See similar textbooks

Similar questions

The weight of newborn babies is normally distributed, with a mean of 3.5 kilograms and a standard deviation of 0.23 kilograms. Find the weight that 14% of newborn babies weigh more than. Round your answer to 2 decimal places. kg
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma.
The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean mu = 125 and standard deviation sigma = 14 . Find the 75-th percentile for the systolic blood pressure.
The scores on a college entrance test have an approximately normal distribution with mean, µ = 84 points and a standard deviation, σ = 5 points. About 68% of the x values lie between what two values?
A soft drink machine is designed to regulate the average discharge of 180 ml per cup.Assume that the amount of soft drink is normally distributed with a standard deviation of 12 ml. (i) Find the percentage of cups containing less than 165 ml. (ii) How many cups out of 500 are expected to contain 190 to 205 ml? (iii) If 35% of the cups have more than k ml of soft drink, find the value of k.
A soft-drink machine is regulated so that it discharges an average of 200 mm/cup. If the amount of drink is normally distributed with a standard deviation equal to 15 mm, what fraction of the cups will contain more than 224mm?
A bottler of drinking water fills plastic bottles with a mean volume of 994 millimeters (mL) with a standard deviation of 5 mL. The fill volumes are normally distributed. What proportion of bottles have volumes less than 995 mL? Use Table A.2 (Normal Distribution Table) and keep four decimal places with your answer.
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma.
The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal with standard deviation ? = 45 milligrams per deciliter (mg/dL). You measure the blood cholesterol of 13 cross-country runners. The mean level is x = 174 mg/dL. Assume that ? is the same as in the general population. How large a sample is needed to cut the margin-of-error in half for a 90% confidence interval of the mean level ? among the cross-country runners?
a sugar company packages sugar in 5kg bags. the amount of sugar per bag varies according to a normal distribution. a sample of 25 bags is selected from the days production and the mean for the day is 4.98 kg and the standard deviation is 0.05 kg. ( use 1-a= 0.95 ) the margin of error for the amount of sugar is?