Statistics Questions

Instructions: Complete the following. Show all work.

(1) According to the Bureau of Labor Statistics through the end of 2017 it was the case that 69.1% of males aged 16 or older were in the labor force (meaning either employed or unemployed but looking for work) and 57.0% of females aged 16 or older were in the labor force. The 2010 US Census determined that males comprise 49.2% and females 50.8% of the US population. Suppose these figures remain the same today and suppose these figures hold true of those aged 16 or older.

a. What is the probability a randomly selected person aged 16 years or older is in the labor force?

b. If a randomly selected person aged 16 years or older is in the labor force what is the probability the person is a female?

(2) A pollster gathers the following information regarding the party affiliations of registered voters and whether they support a new law.

Affiliation	Proportion of Registered Voters	Proportion Who Support Law
Republican Democrat Independent	0.28 0.27 0.43	0.7 0.3 0.5

(a) Calculate the probability that a randomly selected registered voter supports the law.

(b) A randomly selected registered voter supports the law. Calculate the probability that the registered voter is a Republican.

(3) Suppose we toss a coin 100 times. Let X = the number of heads in the 100 tosses.

a. What is the PMF of X?

b. Use R to find the probability X = 50. Write the commands in below.

c. Use R to find the probability X ≤ 50. Write the commands in below.

(4) A box contains five keys, two of which will open a lock. The keys are randomly selected and tried one at a time, until the lock is opened. Keys that do not open the lock are discarded. Let X = the number of the trial on which the lock is opened. Find the expected number of trials until the lock is opened, E[X]. You will need to find the PMF in order to do so.

(5) The file RandomDigits.csv contains the probability distribution of a random variable X. Use this and R to calculate . Write the commands in below.