Example 10.18 A random sample of n = 25 was selected from a normally distributed population. Thepopulation mean is 106 and standard deviation is 12.(a) Find the standard error of the sampling distribution.(b) What is the probability that the sample mean x is greater than 100?(c) What is the probability that the sample mean x will be within ±4 from population mean?

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Answered: Example 10.18 A random sample of n = 25…

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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Q 6. Researchers developed a "dog IQ test" and find that the population of dogs in the United States has a mean score of µ = 20 on this test with a standard deviation of σ = 2. You decide to collect a sample of n = 20, where all of the dogs are poodles, because you suspect maybe poodles aren't really so smart. The mean IQ of your sample of poodles is M = 19. What is the probability of this sample? That is, what is p(M<19)? (Hint: remember the sample size is now n = 20.)
If we have a simple random sample of size n from a population with standard deviation σ, what is the standard deviation of the sampling distribution of the sample mean (x̄)?
Example 42. Show that for the Binomial distribution with parameters n and p : (a) Variance is less than mean ; (b) Variance cannot exceed n/4.
Scores for students on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 108. A random sample of 36 students who took the SAT-I test is selected. Let ?̅ represent the mean score of the sample. 4. The probability that the sample mean score ?̅ is greater than 540 is about (a) 0.9573 (b) 0.5427 (c) 0.6554 (d) 0.0427 (e) 0.17
4. A normal population has the mean of 20 and the variance of 100. A random sample of size n = 69 is selected. (a) Find the standard deviation of the sample mean. (b) How large must the sample be if you want to halve the standard deviation of the sample mean?
Q4. Researchers developed a "dog IQ test" and find that the population of dogs in the United States has a mean score of µ = 20 on this test with a standard deviation of σ = 2. You decide to test a sample of n = 40 dogs to do some research about whether some breeds are smarter. You decide to first test your own dog (or your closest friend's or family member's, if you don't have one). What is the probability that your dog will score an "dog IQ" greater than 25 (which is the cut-off for "Doggie Genius")?
2
True or false?
14
(first part of question is attached) (e) What is the probability that the sample proportion of students of adults living with parents or other relatives is higher than 0.3? (f) What is the probability that the sample proportion of adults living alone is between 0.1 and 0.15?

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