Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.4. (Round youranswers to four decimal places.)A USE SALT(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 14 pins isat least 51?(b) What is the (approximate) probability that the sample mean hardness for a random sample of 41 pins is at least 51?You may need to use the appropriate table in the Appendix of Tables to answer this question.

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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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When asked: "What is the distribution of X ? X ~ N(___,___)." This notation is referring to N, a normal distribution, with the mean given in the first space and the standard deviation in the second space. Remember that the standard deviation of the sample means is different from the population standard deviation. The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation 7 mm. Suppose that 11 individuals are randomly chosen. Round final answers to 4 decimal places. a. What is the distribution of x? x N( b. For the group of 11, find the probability that the average hand length is more than 189. c. Find the first quartile for the average adult male hand length for this sample size. d. For part b), is the assumption that the distribution is normal necessary? Yes No
A. The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. Find the probability that the sum of the 40 values is less than 6,900. (Round your answer to four decimal places.) B. The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. Find the sum that is one standard deviation below the mean of the sums. (Round your answer to two decimal places.) C. The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. Find the sum that is 1.4 standard deviations below the mean of the sums. (Round your answer to two decimal places.)
A study shows that the normal time that a customer occupied a table in a fine dine restaurant is 1.2 hours with a standard deviation of 0.4 hour. A food entrepreneur wants to find the probability that customers occupying 25 tables would have an average time of less than 1 hour. Question: 1. What is the value of the standard deviation of the sampling distribution? A. 0.08 B. 0.4 C. 1.2 D. 1
Suppose x has a normal distribution with mean ? = 53 and standard deviation ? = 7.Describe the distribution of x values for sample size n = 4. (Round ?x to two decimal places.) ?x = ?x = Describe the distribution of x values for sample size n = 16. (Round ?x to two decimal places.) ?x = ?x = Describe the distribution of x values for sample size n = 100. (Round ?x to two decimal places.) ?x = ?x =
3. Assume the heights of students at Champlain College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting a Champlain College studenttallerthan 62.2 inches?A. 0.0668B. 0.0359C. 0.9332D. 0.9641E. 1.0155
Answer number 3 to 5 pls. I don't want to waste my money here
Suppose that the mean and standard deviation of plants height are 130 and 32, respectively, if a random sample of size 49 is slected from these plants, then the probability that their average height is more than 125 is closest to: O a. 0.20 O b.0.86 Oc. 0.26 O d. 0.14 O e. 0.74 Next page
Provide an original example of some practical case where we can use the normal distribution (e.g., IQ scores follow a normal distribution of probabilities with a mean IQ of 100 and a standard deviation of 15 IQ points.). Assign your numbers for mean 70 and standard deviation 30. Make sure 70 is about four times bigger than 30. Then select any number 90 below or above mean 70, but not too far from 70. Find following two probabilities: 1) P(x < a)2) P(x > a)Use the formula z = (a - μ)/σ to calculate your z-value. Please refer to the Appendix Table for the Standard Normal Distribution Hint: To find P(x>a) use formula: P(x>a) = 1 - P(x<a). Describe how to would find P( 65 < x < 25). Provide an original example to illustrate how to find such probabilities.
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 8th percentile of the data is 16 hours. Based on the given information, determine if the following statement is true or false. The first quartile is less than 16 hours.
10) A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 mi/hr. A random sample of 15 vehicles has a mean speed of 43 mil/hr and a standard deviation of 4.4 mi/hr. Assume that speeds follow a normal distribution. What statistical test should be used to test the claim? (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64 Calculate the value of standardized test statistic. (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64 What is the degree of the freedom for the distribution of the test statistics. (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64
Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a standard deviation of 12 millimeters. If 76 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.56 millimeters? Round your answer to four decimal places.
r a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 510 and a standard deviation of 170 . The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 526 . What is the probability that a sample of 40 exams will have a mean score of 526 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

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