The opera theater manager calculates that 15% of the opera tickets for tonight's show have been sold. If the manager is accurate, what is the probability that the proportion of tickets sold in a sample of 690 tickets would differ from the population proportion by more than 4% ? Round your answer to four decimal places.

Twenty people check their hats at a theater. In how many ways can their hats be returned so that

(a) no one receives his or her own hat?

(b) at least one person receives his or her own hat?

(c) exactly one person receives his or her own hat?

a baseball player hits a ball straight up with an initial velocity of 109 miles. Reaches a height of s = 0.03t-0.003t^2 miles after t seconds. What is the speed of the ball when it is at 0.0827 miles off the ground?

(A) A random sample of 18 Kennewick residents looked at how many miles residents were commuting (two ways) to get to work and back. The survey found that the average number of miles they commute had a mean of 23.2 miles round trip, and a standard deviation of 18.1 miles. a.) Calculate a 95% confidence interval for the true mean commute distances of Kennewick residents.

(B) Interpret your interval from part (a.)

The 22,000 students at NCC have mean mileage on their vehicles of µ = 54,000 miles

       with a standard deviation of s = 3,125 miles. Assuming a normal distribution

   a) what is the probability that a randomly selected student has a car with mileage between 55,000
           and 60,000 miles?

b) what percent of student vehicles have mileage above 60,000 miles?

c) how many students have cars with mileage below 50,000?

At the movies: A movie theater is considering a showing of Puppet Master for a 80's thowback night. In order to ensure the success of the evening, they've asked a random sample of 53 patrons whether they would come to the showing or not. Of the 53 patrons, 30 said that they would come to see the film. Construct a 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing.

a) What is the point estimate for the true proportion of interested patrons? (please input a proportion accurate to four decimal places)

b) Complete the interpretation of the confidence interval. Please provide the bounds for the confidence interval in decimal form, accurate to four decimal places, and list the lower bound first.
"We are ... % confident that the true proportion of patrons interested in attending the showing of Puppet Master is between ... and ... "

c) The theater is only willing to show Puppet Master if they are confident that at least 40% of their patrons would be interested in seeing the film. Should they show it?

A movie theater has at most 90 seats available. Each adult movie ticket costs $14, and each child movie ticket costs $8. To make a profit, the theater must bring in more than $852 in ticket sales per show. A) In terms of A and C, write an inequality that represents the restriction on total occupancy. B) In terms of A and C, write an inequality that represents the restriction on total ticket sales. C) Make a graph that represents your inequalities. D) Which scenario satisfies the restriction on total occupancy but does not produce enough ticket sales? E) Which scenario does not satisfy the restriction on total occupancy but does produce enough ticket sales? F) Which scenario does not satisfy the restriction on total occupancy but does produce enough ticket sales? G) Which scenario satisfies the restriction on total occupancy and also produces enough ticket sales? 

part 2

Duque Vergere manages a Do or Die Theater complex called Cinema I, II, III, and IV. Each of the four auditoriums plays a different film; the schedule staggers starting times to avoid the large crowds that would occur if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a normally active day are Poisson distributed and average 210 per hour. To determine the efficiency of the current ticket operation, Duque Vergere wishes to examine several queue-operating characteristics.

d.) What is the average time spent waiting in line to get to the ticket window?
e.) What is the probability that there are more than two people in the system? More than three people? More than four?

The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of27 drivers over the age of 60 and finds that the mean number of miles driven is 22.2. The population standard deviation is miles 3.7. At a=0.05, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the P-value method with a graphing calculator