(05.02 MC)  A nail fabrication machine makes nails with a target length of μ = 2.35 inches. The machine has some variability, so the standard deviation of the length is σ = 0.2 inch. The machine operator inspects a random sample of 10 nails each hour for quality control purposes and records the sample mean diameter, x̄. Assuming the process is working properly, what are the mean and standard deviation of the sampling distribution of x̄? (4 points)

Write the sum using summation notation, assuming the suggested pattern continues. 4 – 12 + 36 – 108 + … (5 points)

(04.06 MC)  Given a normal distribution with a mean of 120 and a standard deviation of 12, what percentage of values is within the interval 96 to 144? (4 points)

State whether the given measurements determine zero, one, or two triangles. C = 37°, a = 16, c = 14 (5 points)

One can be an incredibly fit individual but not be in a state of optimal wellness.  

(05.04 MC)  A zoning board in Pine County is interested in estimating the proportion of its residents in favor of larger school zones in that county. A random sample of Pine County residents was selected. All the selected residents were asked, “Are you in favor of larger school zones in your county?” A 95% confidence interval for the proportion of residents in favor of larger school zones in that county was calculated to be 0.48 ± 0.02. Which of the following statements is correct? (4 points)

(04.02 MC)  A coin is weighted so that the probability of tails is 0.58. The coin is tossed 25 times, and the number of times tails is shown is recorded. This procedure is repeated 150 times with the number of times tails is shown noted each time. What kind of distribution is simulated? (4 points)

(05.04 MC)  A city is interested in building a parking garage in a certain area. Three hundred randomly selected residents from this area were asked, “Do you support the city’s decision to build a parking garage in your area?” Of the 300 residents interviewed, 203 said no, 7 said yes, and 90 had no opinion. A large-sample z-confidence interval, p̂ ± z * , was constructed from these data to estimate the proportion of the residents who support building a parking garage in a certain area. Which of the following statements is correct for this confidence interval? (5 points)

(06.07 LC)  The predicted calories in soda based on grams of sugar are represented by the residual plot. What does the pattern in the residual plot indicate about the type of model? (4 points)

Write the sum using summation notation, assuming the suggested pattern continues. 729 + 1000 + 1331 + 1728 + … + n3 (7 points)