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 average running times of disks produced by Company A is 88.1 minutes and a standard deviation of 6.1 minutes, while Company B obtained a mean running times of 99.3 minutes with a standard deviation of 13.6 minutes. Assume the population are approximately normally distributed. Solve the probability when a random sample of 41 disks from Company B has a mean running times that at most 15 minutes more than the mean running times of a random sample of 32 disks from Company A.Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 80 beats per minute.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 problem
- The height of a certain population of female teenagers is approximately normallydistributed with a mean of 155 cm and a standard deviation of 7 cm. Find the probability that a randomly selected teenager has height (a) between 145 and 165 cm,(b) more than 150 cm, and (c) less than 169 cm. NOTE: Please explain each part, so the problem can be used as a Study GuideTwo devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.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.
- The distribution of heights of a certain breed of terrier dogs has a mean height of 70 cm and standard deviation of 8 cm, whereas the distribution of heights of a certain breed of poodles has a mean height of 30 cm with a standard deviation of 5 cm. 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 60 terriers exceeds the sample mean for a random sample of 80 poodles by at most 44 cm.Assume that women's heights are normally distributed with a mean 64.5 in, and a standard deviation of 2.3 in. (a) if 1 woman is randomly selected, find the probability that her height is less than 65 in.(b) if 46 women are randomly selected, find the probability that they have a mean height less than 65 in.Assume the random variable X is normally distributed with mean =50 and standard deviation =7. Compute the probability. P(X > 36)=
- 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.