We are going to continue using the M&M data to answer these questions.

Assignment Questions

1. Suppose Mars (the company that makes M&Ms) tells us that the number blue candies in each bag is normally distributed with a mean of 10 and a standard deviation of 2.5. Use the equation editor to show your work. Round all probabilities to four decimal places.

1. What is the probability that you open a bag of M&Ms and there are less than 8 blue M&Ms?

• What is the probability that you open a bag of M&Ms and there are more than 14 blue M&Ms?

• What is the probability that you open a bag of M&Ms and the number of blue M&Ms differs from the population mean by more than 1 M&M?

•  What is the probability that you open a bag of M&Ms and the number of blue M&Ms differs from the population mean by less than 2 M&Ms?

• Suppose Mars (the company that makes M&Ms) tells us that the number of yellow candies in each bag is normally distributed with a mean of 9 and a standard deviation of 3. Use the equation editor to show your work to receive full credit. Round all answers to the nearest whole number.

1. My older daughter loves yellow and only wants the bags of M&Ms with a lot of yellow candies. In fact, she says she only wants the bags in the top 10% for the number of yellow candies. What is the minimum number of M&Ms she’ll accept per bag?

• My younger daughter, on the other hand, does not like yellow and only wants the bags of M&Ms with a small number yellow candies. In fact, she says she only wants the bags in the bottom 20% for the number of yellow candies. What is the maximum number of M&Ms she’ll accept per bag?

• Suppose Mars (the company that makes M&Ms) tells us that the number of brown candies in each bag is normally distributed with a mean of 8 and a standard deviation of 2.8. Use the equation editor to show your work to receive full credit. What is the probability that a randomly selected sample of 100 bags of M&Ms will have a mean of less than 11 brown M&Ms per bag? Round your answers to four decimal places.
• To estimate the number of blue candies per bag, students in the class took a random sample of 36 bags and found the sample mean to be 10.53. Construct a 95% confidence interval for the mean number of blue candies per bag. Assume that the population standard deviation is known to be 2.5. Show your work using equation editor or tell what inputs you used in your calculator.

• Determine the minimum sample size of bags needed if we wish to be 85% confident that the sample mean of the number of orange M&Ms per bag is within 2 units of the population mean. Assume the population standard deviation is known to be 3. Show your work using the equation editor.

• To estimate the number of green candies per bag, students in the class took a random sample of 36 bags and found the sample mean to be 9.97 and standard deviation to be 2.78. Assume that the population distribution is approximately normal and the population standard deviation is unknown. Construct a 98% confidence interval for the mean number of green candies per bag. Show your work using equation editor or tell what inputs you used in your calculator.

• In a recent study, students looked at 200 bags of M&Ms and found out 14% of the candies in the bags were red. Find the 90% confidence interval for the true proportion of red candies the bags. Show your work using the equation editor.