General Statistics Probability for Cumulative Distribution
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1. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.
a) What is being measured here? Age of cars
b) In words, define the Random Variable X.
c) Are the data discrete or continuous? continuous
d) The interval of values for X is: (0.5, 9.5)
e) The distribution for X is:
f) Find the cumulative distribution
g) What is the probability that the car is between 1.5 and 4.5 years old?
2. The U.S. Bureau of Labour Statistics reports that the average annual expenditure on food and drink for all families is $5700 (Money, Dec 2003). Assume that the annual expenditures on food and drink are normally distributed and that the standard deviation is $1500.
a. What is the range of expenditures of the 10% of families with the lowest spending on food and drink?
b. What percentage of families spends more than $7000 annually on food and drink?
c. What is the range of expenditures for the 5% of families with the highest annual spending on food and drink?
3. The average annual income American household spends for daily transportation is $6312 (Money, Aug 2001). Assume that amount spent is normally distributed.
a. Suppose that you learn that 5% of American households spend less than $1000 for daily transportation. What is the standard deviation of the amount spent5?
b. What is the probty that a household spends between $4000 and $6000&
c. What is the range of spending for the 3% of households with highest daily transportation cost?
4. A machine fills containers with a particular product. The standard deviation of filling weights is known from the past data to be .6 ounce. If only 2% of the containers hold less than 18 ounces, what are the mean filling weights for the machine? Assume that the filling weights have a normal distribution.
5. When you sign up for the credit card, do you read the contract carefully? In a FinLaw.com survey, individuals were asked, â??How closely do you read a contract for a credit card?â? 44% read every word, 33% read enough to understand the contract, 11% just glance at it, and 4% donâ??t read it at all.
a. For a sample of 500 people, how many would you expect to say that they read every word?
b. For a sample of 500 people, what is the probty that 200 of fewer will say that they read every word in a contract?
c. For a sample of 500 people, what is the probty that at least 15 say they donâ??t read a contract?
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Solution Summary
The general statistics probability for cumulative distribution is examined.
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1. a) Age of cars
b) X is the age of a random car in the staff parking lot
c) Continuous (since time is continuous here)
d) (0.5, 9.5)
e) The probability distribution for a Uniform(a,b) random variable is
f(x) = 1/(b-a) for a <= x <= b
In this case, we would have f(x) = 1/(9.5-0.5) = 1/9 for 0.5 <= x <=9.5
f) The cumulative distribution for a Uniform(0.5, 9.5) random variable is
F(x) = 0 for x < 0.5
F(x) = (x - 0.5)/(9.5-0.5) = (x - 0.5)/9 for 0.5 <= x <= 9.5
F(x) = 1 for x > 9.5
g) F(4.5) - F(1.5) = 1/3 or 0.33
2. Let X ~ Normal(5700, ...
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