If an in-control process follows a normal distribution as x~N(100,2²). The process ismonitored by a control chart with the probability limits of p = 0.025 and sample size of 4,(a) What is Type I error rate?(b) What are the control limits and center line?(c) What is Type II error rate if the processes mean increases by one standard deviation?

Solution: From the given information, x follows normal distribution with mean µ = 100 and standard…

Answered: If an in-control process follows a…

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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Suppose the final exam scores in Statistics and Probability of all SHS students at Laguna State Polytechnic University follow the normal distribution with population mean of 32 and standard deviation of 7. Further, the teacher assumes that the true mean is 32. A random sample of 32 SHS students were selected and their final exam scores were gathered. The computed sample mean is 29. Is there enough evidence to say that the teacher's claim of the true mean is true? Use 0.05 level of significance. Conduct the five steps of hypothesis.
A simple study by Ahmad found a random sample has chosen randomly from certain population that can be described by Normal distribution. (i) Describe the distribution of sample means for a certain sample size. (ii) Explain any effect to the distribution of sample means if the sample size increase.
Lalli long jumper is a teacher in a crowded school here in the city. He is very interested in long jump and he decided to study the long jump ability of the school's students. He held a long jump competition where all the students at the school took part and he measured the length of the students' jumps. Let us now assume that the length of the jump among the students at the school follows a normal distribution with an average of 4 meters and a standard deviation of 1 meter. Lalli randomly selected 100 participants from the long jump competition and asked them if they enjoyed long jump. 62 respondents said they enjoyed long jump. Lalli used the data to create a 95% confidence interval for the proportion of students who enjoy long jump. What is the lower limit of the safety gap? a.) 0.45 b.) 0.52 c.) 0.58 d.) 0.61 e.) 0.71
The line width for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.55 micrometer and a standard deviation of 0.07 micrometer. (A) What is the probability that a line width is greater than 0.72 micrometer? (B) The line width of 80% of samples is below what value?
The reaction time in a chemical process (in seconds) is normally distributed with a mean of 2.94 and variance of 0.68.(a) What is the probability that the reaction time is exactly 2.94 seconds?(b) What is the probability that the reaction time is at least three seconds, given that it is less than 3.5 seconds?
The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.
Diabetes Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean In(plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.64. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. USE SALT (a) If the expected difference is 0.10 In units, then what is the power of such a study if a two-sided test is to be used with a = 0.05? 0.0500 (b) Answer (a) if the expected difference is 0.20 In units. 0.496 (c) How many people would need to be studied to have 80% power under the assumptions in (a)? (Round your answer up to the nearest whole number.) x 398
Mercury is a toxic metal that is used in many industrial applications. Seven measurements, in milligrams per cubic meter, were taken of the mercury concentration in a lake. Assume that the population of measurements is approximately normally distributed. If the sample standard deviation is 0.197, can you conclude that the mean concentration is greater than 1 milligram per cubic meter? Use the 0.02 level of significance. (A) Yes (В) No
(b)The annual rainfall in Dhaka is normally distributed with mean 26 inches and standard deviation 2 inches. (i) What is the probability that the next 2 years the rainfall will exceed 50 inches? Assuming that the rainfalls in different years are independent. (ii) Find the median of rainfall for a year. (iii) What is the chance that annual rainfall will be in between 23 to 30 inches?
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