(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)

(05.01 MC) Mateo is roasting a chicken. He must make sure the chicken has a minimum internal temperature of 165 degrees so that it is safe to eat. Using a thermometer, he takes the temperature of the chicken in three random places. The minimum temperature in the sample is 172 degrees. Identify the population and the sample. (4 points)

(05.02 MC)  The amount of cream sauce on the fettuccine at Al Fred-O’s follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces? (4 points)