Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: The average number of customers waiting. Note: Round your answer to 2 decimal places.   The average time a customer waits. Note: Round your answer to 2 decimal places.   The average time a customer is in the shop. Note: Round your answer to 2 decimal places.   The average utilization of Benny’s time. Note: Round your answer to 1 decimal place.

Back up your data: In a survey backed up their computer's hard drive. The following frequency distribution presents the results. mmissioned by an electronics company, U.S. computer users wereasked how often they Response More than once per month Frequency 844 Once every 1-3 months 521 Once every 4-6 months 229 Once every 7-11 months Once per year or less Never

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 2 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X~ N( b. What is the median recovery time? days c. What is the Z-score for a patient that took 4.3 days to recover? d. What is the probability of spending more than 2.1 days in recovery? e. What is the probability of spending between 3.1 and 4.1 days in recovery? f. The 85th percentile for recovery times is days.

The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009 (t = 3 represents the start of 2003).   A bar graph titled "Percentage of U.S. budget on education" has a horizontal t-axis labeled "Year since 2000" and a vertical axis labeled "Percentage". The bar graph has 7 bars. Each bar is associated with a label and an approximate value as listed below. 3: 6.8% 4: 7% 5: 7% 6: 6.9% 7: 6.5% 8: 6.3% 9: 6.2% The following table shows the percentage of the U.S. discretionary budget allocated to education in 2003, 2005, and 2009 (t = 3 represents the start of 2003). Year t 3 5 9 Percentage 6.8 7 6.2 Find a quadratic model for these three years. (Round your coefficients to two decimal places.) p(t) =          Use your model to estimate the percentage of the U.S. discretionary budget allocated to education in 2007. (Round your answer to two decimal places.)