The typical life of a specific kind of tiny motor is ten years, with a standard variation of two years, according to the manufacturer. All motors that fail while under warranty are replaced at no cost by the manufacturer. In the event that he is only prepared to repair 5 percent of the motors that fail, how long should he provide a guarantee? Assume that the life span of a motor is distributed according to a normal distribution.
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The typical life of a specific kind of tiny motor is ten years, with a standard variation of two years, according to the manufacturer. All motors that fail while under warranty are replaced at no cost by the manufacturer. In the
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- Radon is a gas emitted from the ground that can collect in houses in buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable” Radon levels in a house vary from week to week. In one house, a sample of 6 weeks had the following readings for radon level (in pCi/L): 1.9 2.8 3.9 3.9 4.2 5.7 Find the variance and standard deviation (definitional formula). Show your work using a table.The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1%. When 1.25%o or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b) Find the standard deviation of p. (c) Compute an approximation for P(p N 0.0125), which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. The table contains data for beak heat loss, as a percentage of total body heat loss from all sources, at various temperatures in degrees Celsius. The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) Percent heat loss from beak 1515 3434 1616 3535 1717 3333 1818 3333 1919 3535 2020 4848 2121 5454 2222 5252 2323 4545 2424 5050 2525 4444 2626 5454 2727 5959 2828 6262 2929 6464 3030 6161 Adapted from a graph in…
- Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 14,19,16,14,19,19,14,21,17,17,14,17 Give the p-value and interpret the results. a) p = 0.0012; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. b) p = 0.0012; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0023; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. d) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and…A researcher wants to know whether children with ADHD tend to watch more TV than children who are not diagnosed with the disorder. To examine this, a researcher obtains a sample of n = 36 children (ages 8 to 12 years) who have been diagnosed with ADHD. Each child is asked to keep a journal recording how much time each day is spent watching TV. The average for the sample is M = 4.9 hours/day. Assume that the average TV-watching time for the general population of 8-to-12-year-old children is µ = 4.1 hours/day with σ = 1.8. Is ADHD in children associated with an increased amount of TV-watching?Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 22,17,20,17,17,14,16,21,15,21,15,22 Give the p-value and interpret the results. a) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. b) p = .0562; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0003; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. d) p = 0.0003; Based on 5% significance level, I will reject the…
- The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.5% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p , where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b)Find the standard deviation of p . (c)Compute an approximation for P≥p0.015 , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1%. When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, wherep is the proportion of defective light bulbs in a sample of 4400 when there is no ? malfunction. (b) Find the standard deviation of p. (c) Compute an approximation for P(p 2 0.0125), which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to a certain company for a given employee turnover percentage in a year.
- There is a 3 percent error rate at a specii c point in a production process. If an inspector isplaced at this point, all the errors can be detected and eliminated. However, the inspectoris paid $8 per hour and can inspect units in the process at the rate of 30 per hour.If no inspector is used and defects are allowed to pass this point, there is a cost of $10per unit to correct the defect later on.Should an inspector be hired?An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure " distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group: Distance xx 2 5 4 4 4 6 Days yy 4 21 29 40 47 49 Use a calculator or software to find the following values. (a) Find the mean and standard deviation of xx. MEAN: STANDARD DEVIATION: (b) Find the mean and standard deviation of yy. MEAN: STANDARD DEVIATION: (c) Find the correlation rr between xx and yy. r:Suppose a system is made up of two components that function independently. The components are connected in parallel. One of the components lifetime in days can be expressed by an exponential distribution with A = 0.1. The second component has a lifetime that can be expressed as a lognormal distribution with u = 2.3 and o = 0.1. What is the reliability of the system at 11 days? .5579 .9454 .4421 .0545