In the vehicle speed test, the results were given in the table below: Find: 1. skew modulus 2. kurtosis coefficient Speed range (km/hr 34-35.9 36-37.9 38-39.9 40-41.9 12 13.0 Frequency (fi) 4 6 4 10 Speed range (km/hr 44-45.9 46-47.9 48-49.9 50-51.9 52 Frequency (fi) 22 8 18 17 16 Speed range (km/hr 54-55.9 56-57.9 58-59.9 60-61.9 62.63.0 Frequency (fi) 13 8 6 4
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- A. The approximate standard deviation for the area under a gaussian curve for a population in the figure is .........The value of Young’s modulus (GPa) was determined forcast plates consisting of certain intermetallic substrates,resulting in the following sample observations (“Strengthand Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U-1Mo Intermetallic,” J. of Materials Engr.and Performance, 1997: 46–50):116.4 115.9 114.6 115.2 115.8a. Calculate x and the deviations from the mean.b. Use the deviations calculated in part (a) to obtain thesample variance and the sample standard deviation.c. Calculate s2 by using the computational formula forthe numerator Sxx.d. Subtract 100 from each observation to obtain a sampleof transformed values. Now calculate the samplevariance of these transformed values, and compare itto s2 for the original data.Find kurtosis by using ungroup data given in the picture using quartile deviation, make sure to arrange data before solving question.
- The contingency table shows the results of a random sample of former smokers by the number of times they tried to quit smoking before they were habit-free and gender. At α=0.10, can you conclude that the number of times they tried to quit before they were habit-free is related to gender? Perform the indicated chi-square independence test by completing parts (a) through (e) below.The accompanying specific gravity values describe various wood types used in construction. 0.33 0.35 0.36 0.36 0.37 0.38 0.40 0.40 0.40 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.48 0.49 0.53 0.54 0.54 0.55 0.58 0.61 0.66 0.66 0.67 0.68 0.77 Construct a stem-and-leaf display using repeated stems. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim?
- A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at most 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At α = 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582 What is the critical value of the t?The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993:1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with a mean of 50.2 ksi and a standard deviation of 3.8 ksi. What is the probability that the yield strength is at most 45? (Use 4 decimal places). Show the area of interest in the density curve.A z-score of –1.6 has a corresponding Stanine score of:
- Later, when the medical devices are in full production, a consultant advised that the breaking strength of these devices should not be less than 5.5 psi (pounds per square inch) on average. In the latest batch produced, a technician has noticed a visual defect that may affect the breaking strength of the devices. To investigate, a sample of 8 devices are randomly selected from the batch and the pressure at which they break are recorded as : 6.6, 7.7, 8.0, 6.3, 6.1, 6.3, 6.3, 6.1 these are summarized as having an average breaking strength of 6.68 psi and a standard deviation of s = 0.75 psi. Test, at significance level α = 0.05, whether there is evidence that the average breaking strength of the batch of devices is less than the required breaking strength, by testing the hypotheses: H 0: μ = 5.5 psi H a: μ < 5.5 psi. An estimate of the population mean is . The standard error is . The distribution is (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS=…The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993:1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with a mean of 50.2 ksi and a standard deviation of 3.8 ksi. What is the probability that the yield strength is greater than 60? (Use 4 decimal places) Show the area of interest in the density curve.Consider the following 10 measurements about the cohesion of a soil: 12 kPa, 14 kPa, 15 kPa, 14.5 kPa, 16.0 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa. Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively. (1) Draw the PDF of the cohesion; (2) Evaluate the probability that the cohesion based on the PDF is less than 5 kPa, 10 kPa, and 15 kPa; (3) Assess the effect of the type of distribution on the results.
