At EM Industries a certain machine fills 2-pound (32 ounces) boxes with cereal.  The machine’s actual fill amount for the 2-pound box is found to have an average of 31.9 ounces and standard deviation of 0.40 ounces.  If a box has at least 31.5 ounces of cereal, it considered “acceptable” by the government office of food product regulation.  If a box has more than 32.5 ounces of cereal, it is considered “over-filled” by operations managers at EM Industries.   a)  What is the probability that a randomly filled box is “acceptable”?  What is the probability that a randomly selected box is both, at the same time, “acceptable” and NOT “over-filled”?   b) To monitor the current performance of the box filling process, Mo Nerdstat, quality control manager, decides to measure 20 boxes an hour and track this average performance measure over time.  Develop 3-sigma limits for the current average process and draw the associated averages control chart.

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 352 minutes. For a sample of 54 patients the mean time the drug stayed in the system was 360 minutes. Assume the population standard deviation is 25. Find the p-value of the test statistic

Sarah and her fiancé are planning for their wedding. Distribution of the number of guests coming to the party is normal with the mean 100 and the standard deviation 10. They need to determine how many guests to book for food from a caterer. The caterer makes the following charges: $50 for each guest that is booked in advance; $90 for each guest who is not booked in advance but shows up on the wedding day. The caterer does not offer any refund even if some booked guests may not show up.                                                         Questions: What is the optimal number of guests to book in advance? How much Sarah can save by booking the optimal quantity from a) in advance? What is the expected number of guests that will come to their wedding? If Sarah and her fiancé book 90 guests in advance with the caterer, what is the probability of stock out? If Sarah and her fiancé book 100 guests in advance with the caterer, what is the expected number of meals to be wasted?

An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in Region A is 13.8 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.1 miles per hour. At a = 0.05, can the company support the researcher's claim? Complete parts (a) through (d) below. C. The wind speed in Region A is not less than the wind speed in Region B. D. The wind speed in Region A is less than the wind speed in Region B. Let Region A be sample 1 and let Region B be sample 2. Identify Ho and Ha. Ho: H1 2 H2 Ha: 1 В. z C. z< - 1.645 (c) Find the standardized test statistic z. (Round to two decimal places as needed.)

The average McDonald's restaurant generates $3.3 million in sales each year with a standard deviation of 0.8. Skyler wants to know if the average sales generated by McDonald's restaurants in North Carolina is different than the worldwide average. He surveys 25 restaurants in North Carolina and finds the following data (in millions of dollars): 2.3, 0.9, 2.2, 2.8, 3.1, 3.1, 2.3, 2.6, 2.7, 2.7, 3.1, 3.9, 4.1, 4, 4.5, 1.8, 4.3, 2.7, 3.9, 3.5, 3.2, 1.7, 3.5, 2.9, 2.1 Perform a hypothesis test using a 4% level of significance. Step 1: State the null and alternative hypotheses. Но: ? ? v Ha: ? v (So we will be performing a Select an answer v test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are Select an answer with distribution mean and distribution standard deviation Step 3: Find the p-value of the point estimate. P( ? v ? v P(? v…

A person in the U.S. eats about 25 pounds of M&M's per year with a standard deviation of 3 pounds. How many M&M's would I have to eat to be in the 3rd quartile?

A real estate company, We Rent Houses, regularly conducts survey for average rents in Tampa Bay Area. According to its latest survey, the sample mean rent in 2019 was $950 for Pasco County and $1160 in Hillsborough County. Assume the survey sampled rents for 160 rental units in each County. Also, assume the standard deviation in rents based on the survey was $175 in Pasco County and $230 in Hillsborough County. Compute the valued mannually.  a. Calculate a 95% confidence interval for the population mean rent for Hillsborough County. Provide an interpretation of the confidence interval.  b. Calculate a 95% confidence interval for the population mean for Pasco County. Interpret.  c. Is it possible that the population mean rent in Pasco County is higher than that in Hillsborough County? Explain.

It is generally believed that the heights of adult females in the U.S. are approximately normally distributed with mean 65 inches and standard deviation 4 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university. A. The beds that the university currently purchases are 70 inches long. What proportion of females will be able to fit on the bed while lying perfectly straight (less than 70”)? Draw/Label/Shade a curve with this information and provide the value of the requested proportion. B. What is the height of a female who is in the top 10% for her height? Draw/Label/Shade