Based on historical data, your manager believes that 27% of the company's orders come from first-time customers. A random sample of 112 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.31?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =
(Enter your answer as a number accurate to 4 decimal places.)

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?