24. Three companies sell vitamin B12 supplements locally. All three products are labeled as containing 100µg (micrograms). You analyze 60 tablets from each product and determine the following: Product A Product B Product C μ = 102.1 µg μ = 100.1 μg μ = 103.0 μg o=1.7 µg a=2.4 µg σ= 0.7 µg You want to ensure that 90% of tablets have between 98µg and 104µg of vitamin B12. Assuming that each product's data forms a normal distribution, which products are in the acceptable range? For Product A, P(98 < X < 104) = 86%. For Product B, P(98 < X < 104) = 76%. For Product C, P(98 < X < 104) = 92%.
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- A mutual fund is a professionally managed investmentscheme that pools money from many investorsand invests in a variety of securities. Growth fundsfocus primarily on increasing the value of investments,whereas blended funds seek a balance betweencurrent income and growth. Here is data on theexpense ratio (expenses as a % of assets, from www.morningstar.com) for samples of 20 large-cap balancedfunds and 20 large-cap growth funds (“largecap”refers to the sizes of companies in which thefunds invest; the population sizes are 825 and 762,respectively):Bl 1.03 1.23 1.10 1.64 1.301.27 1.25 0.78 1.05 0.640.94 2.86 1.05 0.75 0.090.79 1.61 1.26 0.93 0.84Gr 0.52 1.06 1.26 2.17 1.550.99 1.10 1.07 1.81 2.050.91 0.79 1.39 0.62 1.521.02 1.10 1.78 1.01 1.15 a. Calculate and compare the values of x, x , , and s forthe two types of funds.b. Construct a comparative boxplot for the two types offunds, and comment on interesting features.4.A new vitamin supplementation program is intended to decrease average resting heart rate inindividuals at risk for hypertension. Assume that a team of researchers are hopeful that restingheart rate in their population will get down to less than 68 bpm, in a population with a standarddeviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273participants in their program and calculates a sample average resting heart rate of 74 bpm.A) Carry out a one sample Z test to determine if the team can conclude that the supplementationprogram is successful in meeting their goal reduction in resting heart rate. Use an α=0.05.B) Construct a 95% Confidence interval about the sample mean, and interpret the result.Life-saving drug: Penicillin is produced by the Penicillin fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows. Day 1: 5.2 5.0 5.4 5.2 5.3 5.0 4.9 5.0 5.2 5.0 4.6 5.3 Day 2: 5.6 4.8 4.9 5.3 5.2 4.9 5.4 5.0 5.4 4.9 5.5 5.4 Day 3: 5.9 4.9 5.3 5.4 5.2 5.5 5.0 5.8 5.5 5.4 5.4 5.1 Construct an ANOVA table. Round your answers to four decimal places as needed. One-way ANOVA: Sugar Concentration Source DF SS MS F P Days Error Total
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