Module 1, Week 2, gretl problem set 2

 

Module 1, Week 2, gretl problem set 2

 

Use gretl to answer the following questions.

 

1. Let  = an odd number coming up when rolling a fair six-sided die.

 

a)     Calculate the probability of an odd number coming up exactly 8 times from 20 rolls.

b)     Calculate the probability of an odd number coming up more than 12 times from 20 rolls.

c)     Calculate the probability of an odd number coming up fewer than 9 times from 20 rolls.

d)     Provide a graph of this probability distribution. Does the graph resemble a normal distribution?

 

 

2. Let  = the number of packages a business receives per week. The average number of packages received per week is 30.

 

a)     Calculate the probability the business receives exactly 33 packages in a week.

b)     Calculate the probability the business receives more than 25 packages in a week.

c)     Calculate the probability the business receives fewer than 35 packages in a week.

d)     Provide a graph of this probability distribution.

 

 

3. Let  = price of a gallon of gasoline. X follows a normal distribution with a mean of 3.5 and variance of 2.5.

 

a)     Calculate the probability the price of a gallon of gasoline is greater than 3.80.

b)     Calculate the probability the price of a gallon of gasoline is less than 2.75.

c)     Calculate the probability the price of a gallon of gasoline is greater than 2.75 and less than 3.80.

d)     Provide a graph of this probability distribution.

 

 

4. Show the central limit theorem. Draw 30 observations from a uniform distribution with a minimum of 0 and a maximum of 1 and calculate the sample mean. Do this 1000 times and plot the distribution of the sample means. Does the distribution of sample means resemble a normal distribution?