The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of ? = 1000 μF and a standard deviation of 80 μF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer’s standards, the machine is working properly if the computed average capacitance falls within 950 μF and 1050 μF. Otherwise, we conclude that ? ≠ 1000 μF. A. Determine the probability of committing a type I error when ? = 1000 μF. B. Determine the probability of committing a type II error when ? = 1080 μF. Hint: Use the sampling distribution of the mean when computing the probabilities.

The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of ? = 1000 μF and a standard deviation of 80 μF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer’s standards, the machine is working properly if the computed average capacitance falls within 950 μF and 1050 μF. Otherwise, we conclude that ? ≠ 1000 μF. A. Determine the probability of committing a type I error when ? = 1000 μF. B. Determine the probability of committing a type II error when ? = 1080 μF. Hint: Use the sampling distribution of the mean when computing the probabilities.

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

For samples of the specified size from the population described, find the mean and standard deviation of the sample meanx. The National Weather Service keeps records of snowfall in mountain ranges. Records indicate that in a certain range, the annual snowfall has a mean of 83 inches and a standard deviation of 14 inches. Suppose the snowfalls are sampled during randomly picked years. For samples of size 49, determine the mean and standard deviation of x A) μ=83; 0x=2 B) μ = 2; σ= 83 Oc C) μ = 83; σ= 14 D) u 14; = 83 =
A survey found that the average hotel room rate in State I is RM88.22 and the average room in State II is RM80.61. Assume that the data were obtained from two samples of 50 hotels each. The population standard deviations were RM5.62 and RM4.83 respectively. At α = 0.05 , can it be concluded that there is a significant difference in the rates?
The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter. If in a couple of years, the mean and the standard deviation of the nished inside diameter of a piston ring change both to dierent values μ and σ, what proportion of rings will have inside diameters exceeding μ + 2.5σ?
A fiber spinning process currently produces a fiber whose strength is normally distributed with a mean of 75 Pa. The minimum acceptable strength is 65Pa. If 10% of the fiber produced by the current method fails to meet the minimum specifications, what is the standard deviation of fiber strengths in the process? If the mean remains at 75 Pa, what must the standard deviation be so that only 1% of the fiber will fail to meet the specifications? Given that the standard deviation is 5Pa, to what value must be mean be set so that only 1% of the fiber will fail to meet the specifications?
Has the number of shoppers who wear masks changed from 2020 to 2021? There are arguments for and against this question. The mean number of masks, u, used by a shopper in Metropolis in 2020 will be compared to the mean number of masks, Hy used by a shopper in Metropolis in 2021. The true values of u, and u, are unknown. It is recognized that the true standard deviations are o, = 19 for the 2020 measurements and o, = 24 for the 2021 measurements. We take a random sample of m = 255 shoppers in 2020 and a random sample of n = 200 shoppers in 2021. The mean number of masks were x= 97 for 2020 and y= 85 for 2021. Assuming independence between the years and assuming masks used by shoppers are normally distributed we would like to estimate x - Hy. What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y? Create a 95% confidence interval for uy - Hy ? ) What is the length of the confidence interval in part c) ? If we let n stay at 200…
a distribution with a mean of u=41 and a standard deviation of 4 is transformed into a standardized distribution with a mean of u=100 and a standardized deviation =20, find the new standardized score for each of the following values from the original population, x=39, x=36, x=45, x=50
a=1 b=8 c=6 d=0
The average zinc concentration recovered from a sample of measurements taken in 40 different locations in a river is found to be 2.5 grams per milliliter. How large a sample is required if we want to be 95% confident that our estimate of ? is off by less than 0.05. Assume that the population standard deviation is 0.25 gram per milliliter.
A nutritionist claims that the mean tuna consumption by a person is 3.6 pounds per year. A sample of 90 people shows that the mean tuna consumption by a person is 3.4 pounds per year. Assume the population standard deviation is 1.11 pounds. At α=0.06, can you reject the claim?
The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o = 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 15 cigarettes of this brand. The sample yields an average of 1.6 mg of nicotine. Conduct a test using a significance level of a = 0.05. (a) The standardized test statistic (b) The critical value (endpoint of Rejection Region) is z* = (c) The final conclusion is OA. The nicotine content is probably higher than advertised. B. There is not sufficient evidence to show that the ad is misleading.
For all parts of this problem, assume that the weights of tomatoes are normally distributed with a mean of 1.8 lbs and a standard deviation of 0.47 lbs.
The coefficients of variations of wages of male workers and female workers are 55% and 70% respectively, while the standard deviations are 22.0 and 15.4 respectively calculate the overall wages of all workers given that 80% of the workers are male?