If the probability of defective bolt is 0.1, find (a) the mean and standard deviation for the distribution of defective bolts in a total of 500, and (b) the moment coefficients of skewness and kur- tosis of the distribution.
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- The length of time it takes to find a parking space is normally distributed with a mean of eight minutes and a standard deviation of two minutes. Find the probability that it takes at most five minutes to find a parking space?Steve, the underpaid graduate student, is interested in determining how many final grades in Dr. Boehring’sclass vary. Steve determines that the standard deviation of final grades in Dr. Tahkstumusch’s class is 7. Steve takes a random sample of 50 final grades from Dr. Boehring’s class and computes a standard deviation of 9.Assume that the final grades in Dr. Boehring’s class are normally distributed. At the 5% significance level, do the data provide sufficient evidence to conclude that the standard deviationσof final grades in Dr. Boehring’sclass are greater than 7? Use the rejection region approach for all of the parts below. (a) Define the appropriate hypotheses (b)State and verify that the proper assumptions hold (c)Use the rejection region approach to perform the test (d) Provide support for your decision regarding the null hypothesis (e) Write a summary of your conclusion in the context of the problemThe random variable X is described by using the gamma distribution with α = 5 and λ = 1. Find the standard deviation of X.
- Weekly salaries of college students in a large city are normally distributed with a mean of 650 dollars and a standard deviation of 65 dollars.Find the probability that a randomly selected weekly salary in this distribution is less than 605 dollars. P(X < 605) =Leave all probabilities as percentages, define x on all problems with data. Simple random samples of high interest (8.9%) and low interest (6.3%) mortgages were obtained. For the 40 high interest mortgages, the borrowers had a mean FICO credit score of 594.8 and a standard deviation of 12.2. For the 40 low interest mortgages, borrowers had a mean FICO credit score of 785.2 and a standard deviation of 16.3. Use an alpha level of 0.01, and a two tailed test of hypothesis to test the claim that the mean FICO score borrowers with a high interest mortgage is the same as the mean FICO score of borrowers with the low interest mortgage.When X is a binomial random variable, the standard deviation of the probability distribution = the square root of npq If X is a binomial random variable, where there are 196 trials, and p = 0.252 find the standard deviation.
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- Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.935°C.The distribution of heights of a certain breed of terrier has a mean of 71 centimeters and a standard deviation of 9 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 29 centimeters with a standard deviation of 5 centimeters. Assuming that the sample means can be measured to any degree of accuracy, find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters. What is the probability? Round to four decimals. Use standard normal distribution table.The probability that a patient recover from a rare blood disease is 0.6. It is known that 100 people have contracted this disease. It is desired to find the probability that less than one half survive. For easier computations, normal distribution is used to approximate this binomial distribution. Find the value of the standard deviation to be used in the computation.
