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## Presentation on theme: "\$100 \$400 \$300 \$200 \$400 \$200 \$100\$100 \$400 \$200\$200 \$500\$500 \$300 \$200 \$500 \$100 \$300 \$100 \$300 \$500 \$300 \$400\$400 \$500."— Presentation transcript:

\$100 \$400 \$300 \$200 \$400 \$200 \$100\$100 \$400 \$200\$200 \$500\$500 \$300 \$200 \$500 \$100 \$300 \$100 \$300 \$500 \$300 \$400\$400 \$500

8.1 Continuous Probability Distributions

8.2 Normal Distribution

8.3 Normal Sampling

8.4 Normal Approximation

VARIOUS QUESTIONS ( Its empty.)

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?

CATEGORY 5 - \$100

CATEGORY 5 - \$200

CATEGORY 5 - \$300

CATEGORY 5 - \$400

CATEGORY 5 - \$500

\$ Answer CATEGORY 1 - \$100 Answers will vary. The height of Humans.

\$ Answer CATEGORY 1 - \$200 a)Discrete probability distribution. b) Discrete probability distribution. c)Discrete probability distribution.

\$ Answer CATEGORY 1 - \$300 Unimodal. Symmetric. Mean = Median = Mode

\$ Answer CATEGORY 1 - \$400 Two Modes. Mean = Median Mean = Median are between the modes

\$ Answer CATEGORY 1 - \$500 Skewed Left – Distribution is shifted to the right. (Mean < Median < Mode) Skewed Right – Distribution is shifted to the Left. (Mean > Median > Mode)

\$ Answer CATEGORY 2 - \$100 a)23.87% b) 52.10% C) 48.8%

\$ Answer CATEGORY 2 - \$200 a)0.069% b) 47.7% c) 73.4%

\$ Answer CATEGORY 2 - \$300 278.47 days.

\$ Answer CATEGORY 2 - \$400 84%

\$ Answer CATEGORY 2 - \$500 1 – 0.9923 =0.00777 =0.77%

\$ 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

\$ Answer a)8.2% b)14.7% c)102,000 boxes. CATEGORY 3 - \$400

\$ 367 CATEGORY 3 - \$500 Answer

\$ CATEGORY 4 - \$100 Answer The normal distribution can be used to approximate the binomial distribution as long as np and nq are both greater than 5.

\$ Answer CATEGORY 4 - \$200 a) 0.6387 b)normal approximation: 0.6387 binomial distribution: 0.6193 The results using a normal approximation are accurate to the nearest tenth.

\$ Answer CATEGORY 4 - \$300 96%

\$ Answer a) The normal distribution approximation is reasonable. b) 24% (approximately for both normal approximation and binomial distribution) CATEGORY 4 - \$400

\$ Answer CATEGORY 4 - \$500 a)0.9507 b)0.0432

\$ Answer CATEGORY 5 - \$100

\$ Answer CATEGORY 5 - \$200

\$ Answer CATEGORY 5 - \$300

\$ Answer CATEGORY 5 - \$400

\$ Answer CATEGORY 5 - \$500

FINAL CATEGORY \$

INSERT FINAL QUESTION (ANSWER) HERE \$

WHAT OR WHO IS THE FINAL ANSWER? FINAL CATEGORY \$

END OF GAME Daily Doubles and usage notes follow...

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Contestant 1 Contestant 2 Contestant 3 \$ \$ \$

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