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# Random Variable, Probability and Distribution

1.The number of pizzas delivered to students each month is a random variable with the following probability distribution:

X 0 1 2 3
P (x) 0.1 0.3 0.4 0.2
A) Find the mean number of pizzas delivered.
B) Calculate the variance in the number of pizzas delivered.
C) Determine the standard deviation.

2. It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.5 days.
A) What proportion of cold sufferers experience symptoms for less than 7.5 days?
B) What proportion of cold sufferers experience symptoms for between 7.5 and 10.5 days?
C) Compute the probability of a cold sufferer experiencing symptoms for more than 14 days.
D) Compute the probability of a cold sufferer experiencing symptoms for less than 5 days?
E) Compute the probability of a cold sufferer experiencing symptoms for between 5 and 8 days?
F) What cold length (number of days of symptoms) is exceeded by only 10% of cold sufferers?

3. The annual report of the U.S. Bureau of Labor Statistics lists the number of employees who receive various types of benefits. From the information in the January 1999 report, the following probabilities were derived.

Dental Care Provided by Employer | Not Provided by Employer
Professional/Technical 0.166 0.094
Clerical/Sales 0.195 0.135
Blue-Collar/Services 0.230 0.180

Let D be the event that a randomly selected employee has dental care provided by their employer.
Let B be the event that a randomly selected employee is a blue-collar/services employee.
A) What is P (B)?
B) What is the probability of the complement of B?
C) What is P (D)?
D) What is P (B and D)?
E) What is P (B or D)?
F) What is P (D|B)?