A softdrink machince can be regulated so that it discharges an average of μ ounces per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 ounces, what should μ be set at so that 6 ounce cups will overflow only 2% of the time?

5. Bone mineral density (BMD) is a measure of bone strength. It is defined as the ratio of bone mass to the cross- sectional area of the bone that is scanned, and it is expressed in units of grams per square centimeter (g/cm²). Recent studies suggest that peak BMD in women is achieved between ages 15 and 40, and BMD declines after age 45. Decreased BMD is associated with increased risk of bone fracture. In a recent study, the impact of regular physical exercise on women in differing stages of BMD development was examined. A simple random sample of 59 women between the ages of 41 and 45 and with no major health problems were enrolled in the study. The women were classified into one of the two following groups, based on their level of exercise activity. • Sedentary: minimal participation in physical exercise in the past three years (This group contained 31 women.) • Walkers: walk at an aerobic pace at least 135 minutes per week during the past three years (This group contained 28 women.)…

Answer d, e, & f.

At a certain high school, every freshman has his or her height The freshman boys have a mean height of 65.2 inches and a standard deviation of 3.2 inches. The freshman girls have a mean height of 63.5 inches and a standard deviation of 2.7 inches. The proportion of of freshman girls has heights between 60 to 65 inches is 0.6133. What is the interpretation of this normal density area? (i) The proportion of freshman having heights between 60 to 65 inches is 0.6133 (ii) The probability that a randomly selected freshman girl have heights between 60 to 65 inches is 0.6133 or 61.33% Oboth (i) and (ii) are correct We can not interpret the given area..

Suppose a variable is Normally distributed with μ=345 and sigma σ=30. What proportion of the data has values between 330 and 345? Use four decimal places in your answer.

Please solve only only the last question.

An author claimed that his annual book sales increased after the year 2000. Past data indicates that the average annual sales for his books are Php 200 M (200 million pesos). The data for the annual sales are normally distributed as shown (in million peso): 2000: 50 2001: 782006: 4002011: 1892016: 83 2002: 3002007: 2902012: 2052017: 132 2003: 2502008: 932013: 3722018: 173 2004: 2002009: 1522014: 4262019: 195 2005: 1852010: 2372015: 252020: 450   Are the author's words true at 98% confidence? In your complete solution, state the null and alternative hypothesis and the complete calculation of test statistic.