A research study performed at checkout lines at Publix Supermarket in South Florida revealed that between 4pm and 7pm on weekdays there is an average of 4 customers waiting in line. What is the probability that you visit a Publix today during this period

1. A research study performed at checkout lines at Publix Supermarket in South Florida revealed that between 4pm and 7pm on weekdays there is an average of 4 customers waiting in line. What is the probability that you visit a Publix today during this period and find:
• No customers waiting?
• 4 customers waiting?
• 4 or fewer customers waiting?
• 4 or more customers waiting?
2. A study on crime indicated that 3.1 car thefts occur each minute in the USA. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution.
• Calculate the probability that exactly 4 thefts occur in a minute
• What is the probability there are no thefts in a minute?
• What is the probability there is at least 1 theft in a minute?
3. The annual sales of playground equipment follow the normal distribution. However, the mean and standard deviation are unknown. 40% of the time sales are more than 470,000 and 10% of the time sales are more than 500,000.
• Calculate the mean and standard deviation.