(b) The capacitance of a batch of capacitors is distributed normally with mean of 22 mF and standard deviation of 1 mF. (i) (ii) What percentage of capacitors can we expect to have a capacitance outside of the limits 22 ± 0.5 mF? The manufacturers stated tolerance of the capacitors is 22 mF ± 10%. In a batch of 1000 capacitors how many would we expect to be inside of the stated tolerance?
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- The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the P-value of the test using either a table of standard normal critical values or…A statistician claims that the standard deviation of the weights of firemen is more than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At alpha=0.05 what is the critical value χ2 for this test?Suppose we want to estimate the concentration (µg/mL) of a specific dose of ampicillin in the urine after various periods of time. We recruit 25 volunteers who have received ampicillin and find they have a mean concentration of 7.0 µg/mL with a standard deviation of 2.0 µg/mL. Assumethe underlying population distribution of concentrations is normally distributed. How large a sample would be needed to ensure that the length of the CI in Problem above is 0.5 µg/mL assuming the sample standard deviation remains at 2.0 µg/mL?
- An article compared the dielectric constants between two types of asphalt, HL3 and HL8, commonly used in pavements. For 42 specimens of HL3 asphalt the average dielectric constant was 5.92 with a standard deviation of 0.15, and for 37 specimens of HL8 asphalt the average dielectric constant was 6.05 with a standard deviation of 0.16. Can you conclude that the mean dielectric constant differs between the two types of asphalt? Find the P-value and state a conclusion. The P-value is . Round the answer to four decimal places. We (Click to select) cannot can conclude that the mean dielectric constant differs between the two types of asphalt.A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the standard deviation in area (in square miles) he has to search in order to find 16 bears?In the manufacture of light emitting diode (LED), different layers of ink are on the optic lens. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X1 and X2 denote the thickness of two different layers of ink. It is known that X1 is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and X2 is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. Let T as the ink total thickness. Give the estimated ink total thickness (in 2 decimal places):
- In the manufacture of light emitting diode (LED), different layers of ink are on the optic lens. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X1 and X2 denote the thickness of two different layers of ink. It is known that X1 is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and X2 is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. Let T as the ink total thickness. Give the estimated ink total thickness: Give the estimated standard deviation of the ink total thickness A lamp with a total ink thickness (T) exceeding 0.2405 mm lacks the uniformity of color that the customer demands. Find the probability that a randomly selected lamp fails to meet customer specificationsthe resistance of a strain gauge is normally distributed with a mean of 100 ohms and a standard deviation of 0.3 ohms. To meet the specification, the resistance must be within the range 100 +- 0.7 ohms. what proportion of gauges is acceptable?The personnel department of a large corporation gives two aptitude tests to job applicants. One measures verbal ability; the other, quantitative ability. From many years' experience, the company has found that the verbal scores (V) tend to be normally distributed with a mean of 50 and a standard deviation of 10. The quantitative scores (Q) are normally distributed with a mean of 100 and a standard deviation of 20, and they appear to be independent of the verbal scores. A composite score, C, is assigned to each applicant, where C=3V+2Q. Applicants whose composite scores are below 375 are automatically rejected. 1) Determine the probability of a random applicant getting automatically rejected.2) If 6 applicants submit resumes, what are the chances that fewer than half will fail the screening test?
- A fiber-spinning process currently produces a fiber whose strength is normally distributed with a mean of 75 N/m2. The minimum acceptable strength is 65 N/m2 . Ten percent of the fiber produced by the current method fails to meet the minimum specification. What is the standard deviation of fiber strengths in the current process? If the mean remains at 75 N/m2, what must the standard deviation be so that only 1% of the fiber will fail to meet the specification? If the standard deviation is 5 N/m2, to what value must the mean be set so that only 1% of the fiber will fail to meet the specification?An obstetrician read that a newborn baby loses on average 7 ounces in the first two days of their life. He feels that in the hospital where he works, the average weight loss of a newborn baby is less than 7 ounces. A random sample of 33 newborn babies has a mean weight loss of 6.2 ounces. The population standard deviation is 1.5 ounces. Is there enough evidence at (alpha) = 0.01 to support this claim? Assume that the variable is normally distributed. Use the critical value method with tables. A. State the hypotheses and identify the claim with the correct hypothesis. B. Find the critical value(s). C. Compute the test value. D. Make the decision. E. Summarize the results.Suppose body temperature is normally distributed with mean of 98.30°F and a standard deviation of 0.76°F. Using these parameters, how often would you expect to measure a body temperature above 100°F?