Chapter 5 Homework I -
Part A -
1. For Binomial distribution
a. Provide a statistical definition
b. Provide a formula for calculations
2. Consider a company where 20% of the employees at a company are college graduates. If a sample of 6 were selected, calculate the probability that exactly 2 employees were college graduates?
Part B -
1. For Poisson distribution
a. Provide a statistical definition
b. Provide a formula for calculations
2. a. Probability is a positive number between ______ and _________
b. Is it possible to have a negative probability?
3. The following chart summarizes daily sales in a 100 day period for a company.
|
1
|
2
|
3
|
4
|
|
Daily Sales
|
Number of days
|
Probability
|
Expected Value = Column 1* Column 3
|
|
1
|
20
|
|
|
|
2
|
30
|
|
|
|
3
|
10
|
|
|
|
4
|
40
|
|
|
|
Total
|
100
|
|
|
a. Calculate the probability for each sales level per day and total probability
b. Calculate the expected value of daily sales
4. Cars arrive at a toll booth at average rate of 8 every minute. On any given day, what is the probability that exactly 3 cars arrive in a one minute period?
Chapter 6 Homework II -
Part A -
1. For the Continuous uniform probability distribution
a. Provide a statistical definition. Include a drawing or picture of this distribution.
b. Define the variables used for calculating continuous uniform probability
c. Provide a formula for calculating probability density
d. Provide a formula for calculating area
e. Provide a formula for calculating the mean (expected value).
2. Production time in Factory A is 15 to 30 minutes to make a widget.
a. What is the probability that it takes between 20 and 25 minutes to manufacture a widget?
b. What is the probability that it takes between 15 and 25 minutes to manufacture a widget?
3. Find the mean or expected value of production time for the following:
a. Production time in Factory A is 15 to 30 minutes to make a widget. What is the expected value (mean) production time for Factory A?
b. Production time in Factory B is 10 to 20 minutes to make a widget. What is the expected value (mean) production time for Factory B?
Part B -
1. For Normal distributions
a. Provide a statistical definition. Include a drawing or picture of this distribution.
b. Provide properties of a normal distribution (Hint - See page 123)
2. For standard score (z-score)
a. Provide a statistical definition
b. Provide a formula to calculate z-score
c. Define the variables used for calculating a z-score
3. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be $2.25 or less? (Hint: Use the Normal tables attached)
4. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be $2.15 or less? (Hint: Use the Normal tables attached)
5. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be between $2.35 and $2.20? (Hint: Use the Normal tables attached)
6. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be between $2.60 and $2.50 (Hint: Use the Normal tables attached)
7. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be at least (greater than) $2.25? (Hint: Use the Normal tables attached)
8. The price of gasoline in Florida is normally distributed with an average price of $2.40 per gallon and a standard deviation of $0.15. What is the probability that the price of gasoline will be at least (greater than) $2.50? (Hint: Use the Normal tables attached)