The weekly demand for Baked Lay's potato chips at a certain Subway sandwich shop is a normally distributed random variable with a mean of 450 and a standard deviation of 80. a. Find the z-score (standardized variable) for a week where 520 bags of chips are sold. b. Show a sketch of the normal distribution to support your answer. On your sketch, label the horizontal axis with the z-scores (-3, -2, -1, 0, +1, +2, +3) and include the appropriate x values that correspond to each of those z-scores. C. Clearly describe at least five characteristics of all normal distributions. In other words, under what conditions can we use a normal distribution?

Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.   Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING...                 x 0.9         A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom, on the left side. The region right of the line is shaded and labeled 0.9. The x-axis below the line is labeled "x".       Question content area bottom Part 1 The indicated IQ​ score, x, is enter your response here. ​(Round to one decimal place as​ needed.)

The amount of caffeine in a sample of five-ounce servings of brewed coffee is shown in the histogram. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. Click the icon to view the histogram. Graph/chart Midpoint x xt Ay 30+ 2 70.5 141 24 14 92.5 1295 25- 24 114.5 2748 20- 7 136.5 955.5 14 15- 3 158.5 475.5 10- 7 ΣΤ- 50 Exf = 5615 5- Find the mean of the data set. 48.5 70.5 92.5 114.5 136.5 158.5 x = 112.3 (Round to the nearest tenth as needed.) Complete the table. Round values to the nearest tenth as needed. Midpoint x (x-x)? (x-x)?f Print Done X-X 70.5 - 41.8 1747.2 3494.5 92.5 1295 85556.3 119787.5

Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67. Last week he won $185. How many standard deviations from the mean is that?