Show that the normal distribution has a relative maximum at x = p. inflection points at x = μ-o and x = μ+o.
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- A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that this average is too high. She selected a random sample of 9 smokers and found that the mean number of cigarettes they smoked per day was 29. The sample standard deviation was 2.3. At =α0.05, is there enough evidence to support her claim? Assume that the population is approximately normally distributed. Use the critical value method and tables.A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that thisaverage is too high. She selected a random sample of 9 smokers and found that the mean number of cigarettes they smoked perday was 29. The sample standard deviation was 2.3. At a =0.05, is there enough evidence to support her claim? Assume that thepopulation is approximately normally distributed. Use the critical value method and tables. h0: h1:A vonsuner group claims that thr mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.5 seconds. A random samoke of 23 sedans has a mean minimum time to travel a quarter mile of 15.3 seconds and a standard deviation of 2.12 seconds. At a=0.10 is there enough evidence to support the consumer group's claim? Assume the population is normally distributed. i) Identify the claim and state Ho Ha H0 ii) Give the P-value: P=0.042, find tge standardized test statistic, t= iii) Decide wheter to reject or faik to reject the null hypothesis. H0 because the P-value
- 50 soil samples from a contruction site were tested for shear strength. The mean of the samples was determined to be 4270kN/m^2. The standard deviation was estimated to be 553kN/m^2. Assuming the data are normally distributed, what is the minimum shear stregnth that can be used for design if we accept a risk that 1% of test sample will fall bellow that minimum strength?An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. What is the probability that the observed depth is within 2 standard deviations of the mean value?Show that when α→q and β remains constant, themoment-generating function of a standardized gammarandom variable approaches the moment-generatingfunction of the standard normal distribution.