Basic Computation:
(a) Suppose n = 33 and p = 0.21. Can we approximate the
(b) Suppose n = 25 and p = 0.15. Can we safely approximate the
(c) Suppose n = 48 and p = 0.15. Can we approximate the
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Understanding Basic Statistics
- Central Limit Theorem: Assume that males have an average run speeds that are normally distributed with a mean of 15 mph and a standard deviation of 3 mph. a. If 1 adult male is randomly selected, find the probability that his run speed is less than 12 mph. b. If 15 adult males are randomly selected, find the probability that they have run speeds with a mean less than 10 mph.arrow_forwardtest the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, andfinal conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry. Does the jury selection system appear to be fair?arrow_forwardA binomial experiment consists of 800 trials. The probability of success for each trial is 0.5.What is the probability of obtaining 390-420 successes? Approximate the probability using a normal distribution. (This binomial experiment easily passes the rule-of-thumb test for approximating a binomial distribution using a normal distribution, as you can check. When computing the probability, adjust the given interval by extending the range by 0.5 on each side.) ... View standard area table. The probability of obtaining 390-420 = ______arrow_forward
- Simulate two Normally distributed random variables X1 and X2 with correlation 0.8, both should have a mean value of 70 and a standard deviation of 8. equation 5.3.2 for formulas that will help you see how to do the simulation. There are other ways to do this as well. Think of X2 as a score on the second test in a class, and X1 as the score on the first exam. a. Analytically find the expected value and variance of `Change = X2 - X1`. b. Use a simulation with n=1000 to find the mean and variance of `Change` using simulation. c. Plot your simulated data on a scatterplot. d. Also plot X1 vs. Change. e. How might regression to the mean cause issues in assessing whether or not a student improved or did worse on the second test compared to the first?arrow_forwardDescribing the sampling distribution of the sample means from an infinite population The heights of male college students are normally distributed with mean of 68 inches and a standard deviation of 3 inches. If 80 samples consisting of 25 students each are drawn from the population, what would be the expected mean and standard deviation of the resulting sampling distribution of the means. With solutionarrow_forwardShear strength measurement for spot welds of a certain type have been found to be have an approximate normal distribution with a standard deviation of 10 psi . If 10 test welds are to be measured , find the approximate probability that the sample means will be within 1 psi of the true population mean.arrow_forward
- Inclusions are defects in poured metal caused by contaminants. The number of (large) inclusions in cast iron follows a Poisson distribution with a rate of 1.9 per cubic millimetre. What is the volume of material to inspect such that the probability of at least one inclusion is 0.99? Please enter the answer to 2 decimal places.arrow_forwardA customer satisfaction survey has been recently conducted by Company A. Most customers were satisfied with their services, with only 5% of them citing some form of dissatisfaction.Suppose a random sample of 200 customers were selected and assuming that normal approximation to the binomial distribution is considered in this case.Let X = “the number of dissatisfied customers”. (i) What are the assumptions needed and special adjustment for the normal approximation to the binomial distribution? Is the approximation valid for this case? Explain.arrow_forwardgenetic experiment involving peas yielded one sample of offspring consisting of 415 green peas and 151 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances, 25% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Question content area bottom Part 1 What are the null and alternative hypotheses? A.Upper H 0 : p not equals 0.25 Upper H 1 : p greater than 0.25 H0: p≠0.25 H1: p>0.25 B.Upper H 0 : p not equals 0.25 Upper H 1 : p equals 0.25 H0: p≠0.25 H1: p=0.25 C.Upper H 0 : p not equals 0.25 Upper H 1 : p less than 0.25 H0: p≠0.25 H1: p<0.25 D.Upper H 0 : p equals 0.25 Upper H 1 : p greater than 0.25 H0: p=0.25 H1: p>0.25 E.Upper H 0…arrow_forward
- Central Limit Theorem The mean serum cholesterol level of a large population of overweight children is 220 milligrams per deciliter (mg/dl), and the standard deviation is 16.3 mg/dl. Assume the serum cholesterol level variable is normally distributed. a. If 1 child is selected, find the probability that the mean will be between 216 and 224 mg/dl. b. If a random sample of 12 overweight children is selected, find the probability that the mean will be between 216 and 224 mg/dl.arrow_forwardSampling distribution of difference between two means is normally distributed.arrow_forwardTrials in an experiment with a polygraph include 99 results that include 23 cases of wrong results and 76 cases of correct results. Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. The test statistic is z = ______ Identify the P-value ______arrow_forward
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