NORMAL DISTRIBUTION Various $100 $300 $300 $300 $300 $200 $400 $400 $400 $500 $ Continuous Distribution NORMAL SAMPLING NORMAL APPROXIMATION
CATEGORY 1 - $100 Describe a real-life example that could have a continuous probability distribution.
CATEGORY 1 - $200 a)Tossing a coin. b) rolling a die c)Dealing five cards from a standard deck Identify possible distribution for the following experiments.
CATEGORY 1 - $300 Describe key features of a Normal probability distribution.
CATEGORY 1 - $400 Describe key features of a BiModal probability distribution.
CATEGORY 1 - $500 Describe the difference between a skewed right and a skewed left probability distribution.
CATEGORY 2 - $100 An electrician is testing the accuracy of resistors that have nominal resistance of 15 Ω(ohms). She finds that the distribution of resistances is approximately normal with a mean of 15.08 and a standard deviation of 1.52. What is the probability that a resistor selected randomly has:- a) a resistance 15 ohms c) has resistance between 14.08ohms and 16.08 ohms.
CATEGORY 2 - $200 Students marks on a test were normally distributed with a mean of 70 and a standard deviation of 5. a)What percent of the student obtained a mark of above 86%? b)What percent of students obtained a B grade (70-80)? c)Determine the mark under which 75% of these students marks occur (this is referred to as the 75 th percentile.)
CATEGORY 2 - $300 To avoid a complete shutdown of the assembly line if a component fails, major manufacturing companies operate on the principle of preventative maintenance. The lifetime of one component is normally distributed with a mean of 325h and a standard deviation of 20 h. How frequently should the component be replaced so that the probability of its failing during operation is <0.01
CATEGORY 2 - $400 Giselle is 168 cm. tall. In her high school, girls height are normally distributed with a mean of 174cm and a standard deviation of 6cm. What is the probability that the first boy Giselle meets at school tomorrow will be taller than she is?
CATEGORY 2 - $500 To run without causing damage, diameters of engine crankshafts for a certain car model must fall between 223.92 mm and 224.08mm. Crankshaft diameters are normally distributed, with a mean of 224mm and a standard deviation of 0.03mm. What percent of these crankshafts are like to cause damage?
CATEGORY 3 - $100 The list below gives the number of patrons per day over a 30-day period during July at a theatre. 127,126,125,132,128,122,156,172,183,171,160,140, 154,160,122,187,185,158,112,145,168,187,117,120,171,171,156,163,168,162. a)Use a method of your choice to assess whether these data are normally distributed. Explain your conclusion. b)Find the mean and standard deviation of these data. c)Determine the probability that a day selected randomly from this sample had at least 160 patrons. State and justify any assumptions you have made.
CATEGORY 3 - $200 Assume that the data are normally distributed. Mickey Mantle played for the New York Yankees from 1951–1968. The table below gives the number of home runs he hit each year during that time. 13,23,21,27,37,52,34,42,31,40,54,30,15,35,19,23,22,18. a)Calculate the mean and standard deviation of these data. b)Estimate the probability that in a particular season Mickey Mantle will hit more than 46 home runs.
CATEGORY 3 - $300 What measures of a normal population can be estimated based on a sample from a normal population?
CATEGORY 3 - $400 A company produces boxes of candy coated chocolate pieces. The number of pieces in each box is assumed to be normally distributed with a mean of 48 pieces and a standard deviation of 4.3 pieces. Quality control will reject any box with fewer than 44 pieces. Boxes with 55 or more pieces will result in exess costs to the company. a) What is the probability that a box selected at random contains exactly 50 pieces ? b) What % of the production will be rejected by quality control as containing too few pieces? c) Each filling machine produces 130,000 boxes per shift. How many of these will lie within the acceptable range?
CATEGORY 3 - $500 The weekly demand for laser printer cartridges at Office Oasis is normally distributed with a mean of 350 cartridges and a standard deviation of 10 cartridges. The store has a policy of avoiding stockouts (having no product on hand). The manager decides that she wants the chance of a stockout in any given week to be at most 5%. How many cartridges should the store carry each week to meet this policy?
CATEGORY 4 - $100 When can the normal distribution be used to approximate the binomial distribution?
CATEGORY 4 - $200 It is estimated that 15% of the Canadian population, given a choice of musical events, would choose a pop/rock concert. a)If 35 Canadians are randomly surveyed, what is the probability that at least 5 of them will choose a pop/rock concert? b)Compare the results from the normal approximation with the results from the calculations using a binomial distribution.
CATEGORY 4 - $300 A manufacturer of toys recalled one of its products when it was discovered that 30% of the toys had a defective part. In a shipment of 600 of these toys, what is the probability that fewer than 200 are defective?
CATEGORY 4 - $400 It is estimated that 89% of Canadian women are 150 cm or taller. If a poll of 400 Canadian women is conducted, what is the probability that more than 360 of them are 150 cm or taller? a)State whether a normal distribution approximation is reasonable for this binomial distribution situation. b)Then, determine the indicated probability.
CATEGORY 4 - $500 A computer- chip manufacturer knows that 72% of the chips produced are defective. Suppose 3000 chips are produced every hour. What is the probability that :- a) at least 800 chips are acceptable? b) exactly 800 chips are acceptable?
$ Answer Data are normally distributed. Explanations will vary, but students should notice that much of the data is clustered around the mean and quite evenly distributed above and below the mean. b) 151.6; 23.31 c)0.3673; Answers may vary, but students should observe that the data are discrete, so continuity correction must be used. CATEGORY 3 - $100
$ Answer CATEGORY 3 - $200 a) 29.78; 11.94 b) 0.08
$ Answer The sample mean, x, and sample standard deviation, s, provide estimates of the underlying parameters, and. CATEGORY 3 - $300
JEOPARDY! Slide Show Setup The font for the question & answer slides is Enchanted; a copy of this font in located in the REAL Jeopardy Template folder or included in the jeopardy_pc.zip file. (This font will need to be installed in the C:/WINDOWS/FONTS folder of the computer running the show.) In order to keep all of the sounds and fonts together, copy the entire REAL Jeopardy Template folder or jeopardy_pc.zip file. To change the categories: –1. Go to the Editmenu and choose Replace… –2. In the Find box, type CATEGORY X (X being 1 through 5) (all caps). –3. In the Replace box, type the category in all caps (for example, PRESIDENTS). –4. Click Replace All… To change the dollar values (for example to create Double Jeopardy): –1. Go to the Edit menu and choose Replace… –2. In the Find box, type $X (the dollar value you want to change). –3. In the Replace box, type the new dollar value (with $). –4. Click Replace All...
JEOPARDY! Slide Show Setup continued To set up the Daily Double: –1. Choose which dollar value(s) to set as Daily Double (normally, Jeopardy has one Daily Double, and Double Jeopardy has two). –2. Go to the Game Board slide (Slide 8), right click once on the dollar value for the appropriate question, choose Hyperlink, and choose Edit Hyperlink. –3. In the Edit Hyperlink window, go to Named location in file and click Browse… –4. In the Hyperlink to Slide window, scroll down to the appropriate slide; Slides 64 and 65 are regular Daily Doubles, Slide 66 is an Audio Daily Double, Slide 67 is a Video Daily Double. Click OK. –5. Go to the Daily Double slide just linked to, and right click once on the answer arrow at the bottom right, choose Hyperlink, and choose Edit Hyperlink. –6. In the Action Settings window, make sure the Hyperlink button (to the left of Hyperlink) is selected, and in the select box underneath choose Slide… –7. In the Hyperlink to Slide window, scroll down to the appropriate question slide (the original slide number of the question). NOTE: Using the Audio and Video Daily Doubles requires adding audio or video/picture clips to the question slides. If you are not familiar with doing this in PowerPoint, do not use those Daily Doubles.
Running the JEOPARDY! Slide Show On the game board with the categories on top (Slide 8), click on the desired dollar value. (The first game board is used only to blink in the dollar values like the show.) The question slide will pop up; the slides are timed with an eight-second timer. At the end of the timer, an alarm will chime. ICONS: –? Go to the answer screen. –House Go back to the game board. –Right Arrow (on Daily Doubles) Go to the question screen. –Right Arrow w/ Bar (on Game Board) Go to the Final Jeopardy category. –Turned-up Arrow Reload question screen after incorrect guess. –$ Go to the Scoreboard slide. –Left Arrow (on Scoreboard) Go to the previous slide.