Suppose that a study is carried out on the performance of the companies WM and TX for which two independent random samples of size 12 of the daily returns are taken fo
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Suppose that a study is carried out on the performance of the companies WM and TX for which two independent random samples of size 12 of the daily returns are taken for each of the companies. It is assumed that the returns have a
a) Calculate the
b) What is the minimum
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- 1. A manufacturer of marble countertops for kitchen countertops manufactures them in Venetian marble slabs measuring 2.4 x 1.8 meters. It is known that the weight of the marble slabs has a normal distribution with an average of 260 kg. and a variance of 81 kg^2.a) 15 of these marble slabs will be shipped in a transport that has a maximum loading capacity of 4 tons. What is the probability that the maximum load capacity of the transport will be exceeded?b) The quality inspector selects a random sample of 10 marble slabs from the production line and wishes to determine what is the probability that the average weight of the sample is more than 255 kg.Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. a) If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 83 beats per minute. b) Why can the normal distribution be used in part (a), even though the sample size does not exceed 30?Suppose that for a random sample of 250 firms that revalued their fixed assets, the mean ratio of debt to tangible assets was 0.629, and the sample standard deviation was 0.177. For an independent random sample of 450 firms that did not revalue their fixed assets, the mean ratio of debt to tangible assets was 0.599, and the sample standard deviation was 0.163. Assuming that the population distributions are normal with equal variances, find a 95% confidence interval for the difference between the two population means. E Click the icon to view a table of upper critical values of Student's t distribution. A 95% confidence interval for the difference between the two population means is (Round to four decimal places as needed.)
- 2. The general weighted average of Mechanical Engineering students from a certain class are approximately normally distributed with mean 1.65 and standard deviation of 0.9. What must their general weighted average be if they want to be in the 1%, 5% and 10% of the class respectively?What important theorem in statistics implies that, for a large sample size, the possible sample proportions of that size have approximately a normal distribution?Consider selecting a random sample of size n=2 (with replacement) from a population consisting of only three numbers 0, 1, 2. (a) Determine the sampling distribution of the sample mean, by listing its possible values as well as their associated probabilities. (b) Repeat (a) for the sample standard deviation.
- 3. The ages of expectant parents at Huntsville Women's and Children's Hospital can be approximated by a bivariate normal distribution with parameters uz = random variable X corresponds to the age of the pregnant woman and the random variable Y corresponds to the expectant father. Determine a) the percentage of pregnant women who are over 30 28.4, ơx = 6.8, µy = 31.6, ơy = 7.4, and p = .82. The %3D b) the percentage of pregnant women who are over age 30 whose husbands (or baby daddy) are aged 35.The diameter of a cylinder follows a normal distribution with mean of 10cm and the variance of 0.04 cm2. a) Construct a Shewhart chart (X-Bar chart) to monitor the process mean of cylinder diameter with a sample size of 9? (Use L = 3) b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift next sample (The first sample after the mean shift)? c) If the process mean stay at 10.5 cm, what is the average number of samples will you see an out-of-control point in the control chart?5. The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimcters. Assume the distributions of both types of breeds are normally distributed. (n) Suppose we are taking a random sample of 64 terriers. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 61 terriers excoedls 75 centimetcrs. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers excoeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.
