Discuss the following:
1. The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&M's, red another 20%, and orange, blue, and green each made up 10%. The rest were brown. If you pick an M&M at random, what is the probability that:
a. it is brown?
b. it is yellow or orange?
c. it is not green?
d. d.. it is striped?
e. Considering all the listed colors, does this data constitute a valid probability distribution?
2. A survey of students in an introductory Statistics class asked about their birth order (1 = oldest or only child) and which college of the university they were enrolled in. The table below lists the data.
Birth Order
1st or an Only 2nd or More Totals
Arts & Sciences 34 23 57
Agriculture 52 41 93
Management 15 28 43
Other 12 18 30
113 110 223
If we were to randomly select one student from this university:
a. Find the probability that the selected student is the oldest or an only.
b. Find the probability that the selected student is enrolled in the College of Arts & Science.
c. Given that the selected student is the "1st or an only", what is the probability that he/she enrolled in the College of Management?
d. Given that the student is enrolled in the College of Agriculture, what is the probability that he/she is "2nd or More in Birth Order"?
e. Find the probability that the selected student is "1st or an only" and enrolled in the College of Management.
f. Find the probability that the selected student earned a Master's Degree or is female?
g. Are the events the selected student earned a Bachelor's Degree and the selected student is male independent events? Explain.
3. Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4" of rain each year with a standard deviation of 4.2". Assume the data is normally distributed.
a. What is the probability that Ithaca will get more than 40" of rain?
b. What is the rainfall amount below which the driest 20% of the years in Ithaca lies?
c. A Cornell University student is in Ithaca for 4 years. If we look at the sampling distribution for those four years, what is the mean and standard deviation of those four years.
d. What is the probability that the average rainfall for those four years is less than 30"
e. What is the probability that the average rainfall for those four years is between 30" and 38.7".
4. Although most of us buy milk by the quart or half gallon, farmers measure daily production in pounds. Ayrshire cows average 47 pounds of milk a day with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 43 pounds with a standard deviation of 5 pounds. Assume the milk production for these breeds is normally distributed.
a. We select an Ayrshire at random. What is the probability that she produces more than 50 pounds of milk a day?
b. A farmer has 20 Jerseys. What is the probability that the average production of this herd exceeds 45 pounds of milk a day?
c. What is the probability that this herd of Jersey produces an average of less than 38 pounds of milk per day?
d. A neighboring farmer has 10 Ayrshire cows. What is the probability that his herd has an average daily milk production greater than greater than 50 pounds.
e. What is the probability that the mean milk production of this herd of Ayrshire cows is within 10 pounds of the mean?