Ch. 6 Practice 1) Suppose the amount of time students take to complete the final programming assignment in a computer science course is normally distributed with a mean of 24.7 hours and a standard deviation of 4.8 hours. Find the z-score of a randomly selected student who took 17.6 hours to complete that assignment. Express the answer as a decimal value rounded to the nearest hundredth. 2) The display below illustrates a normal distribution shown with z-scores on the horizontal axis. Which inequality marks the proportion of the display shaded in red? 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 O z > -0.5 O -0.5 0.53) Suppose the life spans of a particular brand of car battery are normally distributed with a mean of 44.7 months. When a battery of this brand is randomly selected, the probability it lasts more than 53.4 months is 0.27. Find the probability a randomly select battery of this brand lasts less than 53.4 months. Express the answer as a decimal value rounded to the nearest hundredth. 4) The advertised fuel economy of the 2020 Toyota Camry model with 4 cylinders and a 2.5 liter engine is 34 miles per gallon (mpg). The observed fuel economy among drivers of that vehicle is slightly lower. The distribution of those values is approximately normal with a mean mpg of 33.1. When a model of this vehicle is randomly selected, the probability that its fuel economy reading is 2.1 mpg above the mean is 0.34. Find the probability a randomly selected model of this vehicle has a fuel economy reading 2.1 mpg below the mean. Express the answer as a decimal value rounded to the nearest hundredth. 5) The distances golf balls travel under laboratory testing conditions are normally distributed. The mean is 312 yards. The probability the golf ball travels further than 319 yards is 0.26. Find the probability a randomly selected golf ball travels between 305 yards and 319 yards. Express the answer as a decimal value rounded to the nearest hundredth. 5) When soda is added to a 12-ounce cup rst lled with ice, the actual amount of soda in the cup is naturally less than the cup capacity. Suppose the actual amounts of soda in the cups are normally distributed with a mean of 6.4 ounces and a standard deviation of 0.37 ounces. Find the probability a randomly selected 12-ounce cup contains at least 7.1 ounces of soda. Express the answer as a decimal value rounded to the nearest thousandth. 7) Due to a consumer protection law which penalizes manufacturers if their products are under lled (contains less than the advertised amount), some manufacturers deliberately overll slightly. For example, the label on a bag of sugar shows its weight to be 1 kilogram (1000 grams). Assume the distribution of the weights of sugar in the bags is approximately normal with a mean of 1038 grams and a standard deviation of 23 grams. Find the probability a randomly selected bag contains at most 1000 grams of sugar. Express the answer as a decimal value rounded to the nearest thousandth. 8) The standard normal distribution has a mean of 0 and a standard deviation of 1. Find the z-score for the 82nd percentile. Express the answer as a decimal value rounded to the nearest hundredth