(05.02 MC)  The amount of marinara sauce on the spaghetti at Pasta Infusion follows a Normal distribution, with a mean of 3.25 ounces and a standard deviation of 0.2 ounce. A random sample of 10 plates of spaghetti is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.3 ounces? (4 points)

(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)

(05.01 LC)  Tiara, a quality assurance inspector at a chocolate factory, checks for product quality using a random sample of 18 pieces of chocolate from a batch of 60, with 17 white chocolates and 43 dark chocolates. Let p̂ be the proportion of white chocolates in the sample. Part A: Is the 10% condition met in this case? Justify your answer. (5 points) Part B: Is the Normal condition met in this case? Justify your answer. (5 points) (10 points)

Write the sum using summation notation, assuming the suggested pattern continues. 8 + 27 + 64 + 125 + … + n3 (7 points)

A mother is in with her full-term baby for a 2-week check. She plans to breastfeed full-time for the first 4 months of life and then wean fairly quickly as she returns to work. For now, you would recommend supplementation as follows:

Find an equation for the nth term of the sequence. -1, -4, -16, -64, … (7 points)  

(05.02 LC)  The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? (4 points) The distribution of the sample mean is exactly Normal. The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal.

(05.02 LC)  The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are false? (4 points) The distribution of the sample mean is exactly Normal. The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal.

(05.01 MC)  Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂? (4 points)

Write the sum using summation notation, assuming the suggested pattern continues. 8 + 27 + 64 + 125 + … + n3 (7 points)