MATH 221 Week 4 Quiz (100% Correct Answers)

Question: (CO 3) The speed of cars on a stretch of road is normally distributed with an average 48 miles per hour with a standard deviation of 5.9 miles per hour. What is the probability that a random ly selected car is violating the speed limit of 50 miles per hour? Question: (CO 3) A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 16 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store. Question: (CO 3) The monthly utility bills in a city are normally distributed with a mean of $121 and a standard deviation of $41. Find the probability that a randomly selected utility bill is between $110 and $130. Question: (CO 3) A restaurant serves hot chocolate that has a mean temperature of 175 degrees with a standard deviation of 8.1 degrees. Find the probability that a randomly selected cup of hot chocolate would have a temperature of less than 164 degrees. Would this outcome warrant a replacement cup (meaning that it would be unusual)? Question: (CO 3) The yearly amounts of carbon emissions from cars in Belgium are normally distributed with a mean of 13.9 gigagrams per year and a standard deviation of 3.5 gigagrams per Find the probability that the amount of carbon emissions from cars in Belgium for a randomly selected year are between 11.5 gigagrams and 14.0 gigagrams per year. Question: (CO 3) On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 12.2 inches. Find the probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%? Question: (CO 3) A process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. If a randomly selected minute has 128 rotations per minute, would the process be considered in control or out of control? Question: (CO 3) The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 6.7, 6.1. Is the process in control or out of control and why? Question: (CO 3) The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 2.9 years. What warranty should be provided so that the company is replacing about 6% of their blenders sold? Question: (CO 3) A puck company wants to sponsor the players with the 10% quickest goals in hockey games. The times of first goals are normally distributed with a mean of 12.56 minutes and a standard deviation of 4.91 minutes. How fast would a player need to make a goal to be sponsored by the puck company? Question: (CO 3) A stock’s price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 15% of What is the most you would be willing to pay for the stock? Question: (CO 3) The times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of 15.9 minutes. A random sample of 60 customers has a mean of 36.1 minutes. Would this outcome be considered unusual, so that the store should reconsider its displays? Question: (CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20 ounces and a standard deviation of 0.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than unces? Question: (CO 3) Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9. What is the probability that the mean of 8 randomly selected scores is less than 161? Question: (CO 3) The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2000. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $73500? Question: (CO 3) In captivity, a male lion grows to weight about 420 lbs with a standard deviation of 35 lbs. A zoo would like to have a lion that is in the largest 15% of male lions based on How much should a male lion weigh for the zoo to – obtain the male lion? Question: (CO 3) Chairs from a manufacturer have an average height from the leg to the top of the seat of 19 inches with a standard deviation of 0.5 inches. How tall would a chair need to be from the assembly line to be unusually short? Question: (CO 3) The average area of a bedroom in a home is 219 square feet with a standard deviation of 32.5 square feet. What is the largest a bedroom can be and be among the Show Less