AssignmentAfter collecting considerable data, the engineers decided to model the variation inshaft diameter as a normal distribution with mean 10.1 mm and standard deviation2.7 mm.(a) For the next shaft, what is the probability that its diameter is between 8.5 mmand 13.0 mm?(b) According to the normal model, what proportion of the shafts have diameterbetween 8.5 mm and 13.0 mm?(c) What proportion of the shafts have diameter greater than 15.I mm?

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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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3. Normal Distribution and Z - Scores Assume a normal distribution for a population of scores for a standardized exam. The average exam score is 70, and the standard deviation is 5. Jeff's exam score is 63. a) What percentage of the population has an exam score greater than Jeff's? b) What percentage of the population has an exam score greater than Jeff's but less than the score of 74? c) If 10,000 people were given the exam, how many of them have an exam score less than Jeff's?
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.
a standarized reading exam has a mean score of 80 with standard deviation =12. the distribution of scores i normal. Find the percentage of test takers who got: a) under 80 b) between 68 and 92 c) over 100 d) over 25 e) what is the 40th percentile?
Steel rods are manufactured with a mean length of 26centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.05 cm. Complete parts (a) to (d). (a) What proportion of rods has a length less than 25.9cm?
Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a standard deviation of 12. What proportion of people has diastolic blood pressures less than 80? A)0.661 B)0.338 C)0.50 D)0.75
d) For a standard normal distribution, find the probability a score is lower than 2.37 standard deviations above the mean? e) For a standard normal distribution, find the probability a score is between the mean and 2.37 standard deviations above the mean?
A normal distribution of scores has a standard deviation of 10 and a mean of 0. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. b) A score that is 10 points below the mean. c) A score that is 15 points above the mean d) A score that is 30 points below the mean. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160. a. Convert Einstein’s IQ score to a z score.
Using this data set What is the standard error of the relevant distribution? Ignoring that the number of men in the 2012 Survey was about 17,675, and the number of women was about 18,634, assume the samples were 100 men and 100 women in each Survey My worked solution is: P1: men proportion change = 15.5/100 = 0.155 N1 = 100 P2: women proportion change = 57.9/100 = 0.579 N2 = 100 {[0.155 * (1 - 0.155) /] + [0.579 * (1 - 0.579) / 100]} = 0.0037 Standard Error = 0.0037 is this correct?
7. Ecological Applications study on the development following wildfires in the Pacific Northwest. One variable of interest to the researcher was tree diameter at breast height 110 years after the fire. The population of Douglas fir trees was shown to have an approximately normal distribution with mean tree diameter ? = 50 centimeters (cm) and ? = 14 cm. Find the diameter, d, such that 20.9% of the Douglas fir trees in the population have diameters that exceed d. published a of forests

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