(a) In a survey conducted by a mail order company a random sample of 200 customers yielded 172 who indicated that they were highly satis ed with the delivery time of their orders. Calculate an approximate 95% con dence interval for the proportion of the company's customers who are highly satis ed with delivery times.
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8. (a) In a survey conducted by a mail order company a random sample of 200 customers
yielded 172 who indicated that they were highly satis ed with the delivery time of
their orders. Calculate an approximate 95% con dence interval for the proportion
of the company's customers who are highly satis ed with delivery times. (3)
(b) A random sample of size 49 from a
terval for the population mean as (30; 50).
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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 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 a psychological testing experiment, 25 subjects are selected randomly and their reaction time, in seconds, to a particular stimulus is measured. Past experience suggests that the variance in reaction times to these types of stimuli is 4 sec2 and that the distribution of reaction times is approximately normal. The average time for the subjects is 6.2 seconds. Give an upper 95% bound for the mean reaction time.
- imagine a large class where nearly everyone scores between 83.84%, with hardly any dispersion beyond this narrow range (so it would appear to have a very narrow peak). How would your describe this distribution of data in terms of kurtosis?Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 14.2 g/dL. Research shows that exactly 95% of healthy females haha a hemoglobin level of below 16.2 g/dL. What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. 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 in the total thickness. a.) Find the estimated ink total thicknessb.) Find the estimated standard deviation of the ink total thickness
- Suppose that the weight of an newborn fawn is Uniformly distributed between 2.5 and 3.9 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. Find the 61st percentile.A manufacturer makes screws with a mean diameter of 0.15 cm (centimeters) and a range of 0.10 cm to 0.20 cm; within that range, the distribution is uniform. Suppose you repeatedly draw samples of size 100 and calculate their mean. Applying the central limit theorem, what is the distribution of these sample means? a the standard deviation of the distribution is 0.01 b the standard deviation of the distribution is 0.04 c the standard deviation of the distribution is 0.03 d the standard deviation of the distribution is 0.05In an Omani factory, a machine that produces "W-product" has been set so that the true average diameter of the "W-product" it produces is 0.602 in. If its diameter is within 0.04 in. of this target value, this is acceptable. Suppose, however, that the setting has changed during the course of production, so that the products have normally distributed diameters with mean value 0.601 in. and standard deviation 0.002 in. What percentage of the "W-product" produced will not be acceptable
- According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.07°F and a standard deviation of 0.55°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean?Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 14.1g/dL. Research shows that exactly 95% of healthy females have a hemoglobin level below 16.2 g/dL. What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 14.2 gmdL. Research shows that exactly 95% of healthy females have a hemoglobin level below 15.8 gmdL . What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places. _ gmdL?=
