Chapter 6 part 2 practice Question 1 Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is -1.3. What is x? 58.7 61.3 62.6 57.4 54.7 Question 2 The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor will not have a net loss is ____________ . 0.4772 0.0228 0.9544 0.9772 1.0000 Question 3 A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. If 5 students received F's, how many total students were there in the class? 89 55 200 Cannot be determined from the information given. Question 4 The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 5.1 ounces? 4.278 4.409 3.455 5.922 Question 5 The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers? 5.5 1,166 550 48.18 Question 6 During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. 80% of the households spent more than what amount? $7.30 $7.38 $9.06 $9.14 Question 7 A manufacturer of personal computers sets tests competing brands and finds that the amounts of energy they require are normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25% and the highest 30% are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining sets? [269.76 300.24] [278.90, 288.55] [280.22 289.78] [280.22 300.24] Question 8 The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation? 4,000 2,500 2,000 4,100 Question 9 A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received weekly be greater than 210 or Less than 180? .6915 .4672 .1915 .1587 Question 10 The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. a. What is the probability that a randomly selected bill will be at least $39.10? b. What percentage of the bills will be less than $16.90? c. What are the minimum and maximum of the middle 95% of the bills? d. If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day? Press Tab to enter the content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor Use arrow keys to select functions Bold Italic Underline Font family Font size Text Color Bullet List Number List Toggle Spell Checker Insert/Edit Link Remove Link Bold Italic Underline Strikethrough Format Font family Font size Bullet List Number List Text Color Highlight Remove Formatting Cut Copy Paste Find Undo Redo Align Left Align Center Align Right Align Full Indent Outdent Superscript Subscript Insert/Edit Link Remove Link Direction Left to Right Direction Right to Left Line Horizontal Rule Insert Nonbreaking Space Character Toggle Spell Checker Record from Webcam Launch Math Editor Insert Mashup Show Nonprinting Characters Blockquote Symbol Emotions Anchor Insert/Edit Table Table Row Properties Table Cell Properties Insert Row Before Insert Row After Delete Row Insert Column Before Insert Column After Delete Column Merge Table Cells Split Merged Table Cells HTML Code View Edit CSS Style Preview Help Full Screen Show More Path: Words:0 Question 11 A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation. Press Tab to enter the content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor Use arrow keys to select functions Bold Italic Underline Font family Font size Text Color Bullet List Number List Toggle Spell Checker Insert/Edit Link Remove Link Bold Italic Underline Strikethrough Format Font family Font size Bullet List Number List Text Color Highlight Remove Formatting Cut Copy Paste Find Undo Redo Align Left Align Center Align Right Align Full Indent Outdent Superscript Subscript Insert/Edit Link Remove Link Direction Left to Right Direction Right to Left Line Horizontal Rule Insert Nonbreaking Space Character Toggle Spell Checker Record from Webcam Launch Math Editor Insert Mashup Show Nonprinting Characters Blockquote Symbol Emotions Anchor Insert/Edit Table Table Row Properties Table Cell Properties Insert Row Before Insert Row After Delete Row Insert Column Before Insert Column After Delete Column Merge Table Cells Split Merged Table Cells HTML Code View Edit CSS Style Preview Help Full Screen Show More Path: Words:0 Question 12 The life expectancy of Timely brand watches is normally distributed with a mean of four years and a standard deviation of eight months. a. What is the probability that a randomly selected watch will be in working condition for more than five years? b. The company has a three-year warranty period on their watches. What percentage of their watches will be in operating condition after the warranty period? c. What is the minimum and the maximum life expectancy of the middle 95% of the watches? d. Ninety-five percent of the watches will have a life expectancy of at least how many months? Press Tab to enter the content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor Use arrow keys to select functions Bold Italic Underline Font family Font size Text Color Bullet List Number List Toggle Spell Checker Insert/Edit Link Remove Link Bold Italic Underline Strikethrough Format Font family Font size Bullet List Number List Text Color Highlight Remove Formatting Cut Copy Paste Find Undo Redo Align Left Align Center Align Right Align Full Indent Outdent Superscript Subscript Insert/Edit Link Remove Link Direction Left to Right Direction Right to Left Line Horizontal Rule Insert Nonbreaking Space Character Toggle Spell Checker Record from Webcam Launch Math Editor Insert Mashup Show Nonprinting Characters Blockquote Symbol Emotions Anchor Insert/Edit Table Table Row Properties Table Cell Properties Insert Row Before Insert Row After Delete Row Insert Column Before Insert Column After Delete Column Merge Table Cells Split Merged Table Cells HTML Code View Edit CSS Style Preview Help Full Screen Show More Path: Words:0 Question 13 A local market research company has been hires to collect data about the salaries of recent college graduates. Based on their research, on average students graduating from business school with a degree in analytics earn $90,000 and with a standard deviation of $28,000. We can also assume that these salaries are normally distributed. In order to maintain the reputation of a "high paying degree" the company that conducts the study wants to peronally interview those students earning in the upper 1.79% of the salary range. If they only want to talk to these highest paid graduates, what is the minimum amount they must earn in order to the included in the survey? Question 14 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. What is the probability that a randomly selected computer will have a price of at least $1,530? 0.0668 0.5668 0.4332 1.4332 Question 15 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount? 62% 0.62% 0.062% 99.38% Question 16 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM? 185,500 85,500 513,000 Question 17 A local market research company has been hires to collect data about the salaries of recent college graduates. Based on their research, on average students graduating from business school with a degree in analytics earn $90,000 and with a standard deviation of $28,000. We can also assume that these salaries are normally distributed. In order to maintain the reputation of a "high paying degree" the company that conducts the study exempts the lowest 6.68% of students salaries from its survey. If they do not include the data from this 6.68%, what is the maximum salary that would be excluded from the survey? (HINT: This is the same value as the MINIMUM SALARY that they would INCLUDE in their survey)