Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in an article. 180.6 181.7 180.9 181.5 182.5 181.5 181.4 182.1 182.1 180.2 181.6 180.4 Compute the following. (Round your answer to two decimal places.) (a) the sample range (in .C) 2.3 OC (b) the sample variance s from the definition [Hint: First subtract 180 from each observation.] 52 = 0.58875 X (c) the sample standard deviation S= 0.7665 (d) $2 using the shortcut method 52 = 0.5875 XA mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, Intermediate, and long- term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows. Money-market 23% High-risk stock 16% Short bond 14% Moderate-risk stock 25% Intermediate bond 5% Balanced 12% Long bond 5% A customer who owns shares in just one fund is randomly selected. (a) What is the probability that the selected individual owns shares in the balanced fund? (b) "What is the probability that the individual owns shares in a bond fund? (c) What is the probability that the selected individual does not own shares in a stock fund?The shear strength of each of ten test spot welds is determined, yielding the following data (psi). 367 374 362 384 415 389 375 358 407 409 (a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.) average 384 psi standard deviation 189.78 X psi (b) Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [Hint: What is the 95th percentile in terms of & and ? Now use the invariance principle.] (Round your answer to two decimal places.) psi (c) Suppose we decide to examine another test spot weld. Let X = shear strength of the weld. Use the given data to obtain the mle of P(X