Sampling Distributions and Gold Application

Darren Starns, an AP Statistics teacher, guides students through an investigative task focusing on probability calculations related to a jewelry company's gold coating process. The session covers calculating probabilities for individual necklaces and sample means, exploring variation using sample range, and assessing machine performance. Students are encouraged to attempt questions before proceeding and to use both traditional and technological methods for calculations.

What is the main focus of the investigative task discussed in the video?

• A jewelry company's machine applying gold to necklaces

• A car manufacturing plant's painting process

• A bakery's machine applying icing to cakes

• A factory's machine assembling watches

In Part A, what is the mean amount of gold applied to a necklace when the machine is working properly?

• 400 milligrams

• 300 milligrams

• 200 milligrams

• 500 milligrams

What is the standard deviation of the gold applied to a necklace in Part A?

• 5 milligrams

• 7 milligrams

• 3 milligrams

• 9 milligrams

In Part B, what is the sample size used to calculate the sample mean?

• 4 necklaces

• 3 necklaces

• 2 necklaces

• 1 necklace

What is the probability that the sample mean amount of gold applied is greater than 303 milligrams?

• 0.0981

• 0.3981

• 0.1981

• 0.2981

In Part C, how does the sampling distribution of the sample range change as the population standard deviation increases?

• The shape becomes left-skewed

• The center moves to the right

• The center moves to the left

• The variability decreases

What is the shape of the sampling distribution of the sample range when the population standard deviation is five?

• Uniform

• Symmetrical

• Right-skewed

• Left-skewed

In Part D, what is the sample range of gold applied when the machine is working properly?

• 5 milligrams

• 10 milligrams

• 15 milligrams

• 20 milligrams

Does a sample mean of 303 milligrams indicate that the machine is not working properly?

• No, it is extremely rare

• Yes, it is highly unusual

• No, it is not unusual

• Yes, it indicates a malfunction

What is the probability of obtaining a sample range of 10 milligrams or greater when the machine is working properly?

• 0.02

• 0.20

• 0.50

• 0.80