A hormal distribution (continuous curve and bell shaped) can be used to approximate a binomial distribution...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A hormal distribution (continuous curve and bell shaped) can be used to approximate a binomial distribution (discrete and not continuous) provided that np > 5 and ng < 5. Given this fact, complete the following tasks: a). Check whether this is the case with Q19. If so, complete part b onwards Complete the table on the next page using EXCEL. Include a hardcopy of your results. Note that the corresponding probabilities P(z) are obtained from Table A and Table B b). Construct the normal distribution [ P(z) versus z(x) ] curve using EXCEL. Include a hard copy of your graph. c). d). Using the normal distribution, find the probability of getting 10 heads or more . Osing the normal distribution, find the probability of getting less than 4 headS Note: A Continuity Correction Error is required when a Normal approximation to a Binomial Distribution is used. That is, the addition of 05 and/or subtraction of 0.5 from the valde(s) of x is required, where x is the number of successes (Binomial) in n trials Pnormal(9.5 sx < 10.5) = Pbinomial(x = 10) Pnormal(x 29.5) = Pbinomial(x 2 10) Pnormal(x < 4.5) = Pbinomial(x < 4) P(z) is an approximate probability only, taken from Table A and Table B below Binomial Normal x-0.5 x' + 0.5 z(x) = P(z) x' P(x') (x) -0.5 0.5 0.5 1.5 1.5 2.5 2.5 3.5 20.5 19.5 20.5 20 Binomial Distribution con't Definition The formula on the previous page has three distinct parts: Firstly, nCx determines the number of ways a success can occur, secondly, (p)* is the probability of getting x successes, and finally, Soh wori nl (1 – p)* is the probability of getting n- X failures . The mean of a binomial distribution is given by u = n.p Sles Or to od e nl The standard deviation of a binomial distribution is given by o = np(1 – p) 19). Construct the sample space for tossing a coin 20 times. Complete the following tasks: Let x = number of heads y co (8/ a). Construct a table consisting of Outcomes (x) versus Probability [P(x)] Use the table above to construct a histogram of the probability distribution. What do you notice? Use EXCEL to achieve this and include a hardcopy in your assignment. b). c). Determine the mean and standard deviation of the outcomes. d). How many standard deviations will most of the outcomes for 3 heads fall within? A hormal distribution (continuous curve and bell shaped) can be used to approximate a binomial distribution (discrete and not continuous) provided that np > 5 and ng < 5. Given this fact, complete the following tasks: a). Check whether this is the case with Q19. If so, complete part b onwards Complete the table on the next page using EXCEL. Include a hardcopy of your results. Note that the corresponding probabilities P(z) are obtained from Table A and Table B b). Construct the normal distribution [ P(z) versus z(x) ] curve using EXCEL. Include a hard copy of your graph. c). d). Using the normal distribution, find the probability of getting 10 heads or more . Osing the normal distribution, find the probability of getting less than 4 headS Note: A Continuity Correction Error is required when a Normal approximation to a Binomial Distribution is used. That is, the addition of 05 and/or subtraction of 0.5 from the valde(s) of x is required, where x is the number of successes (Binomial) in n trials Pnormal(9.5 sx < 10.5) = Pbinomial(x = 10) Pnormal(x 29.5) = Pbinomial(x 2 10) Pnormal(x < 4.5) = Pbinomial(x < 4) P(z) is an approximate probability only, taken from Table A and Table B below Binomial Normal x-0.5 x' + 0.5 z(x) = P(z) x' P(x') (x) -0.5 0.5 0.5 1.5 1.5 2.5 2.5 3.5 20.5 19.5 20.5 20 Binomial Distribution con't Definition The formula on the previous page has three distinct parts: Firstly, nCx determines the number of ways a success can occur, secondly, (p)* is the probability of getting x successes, and finally, Soh wori nl (1 – p)* is the probability of getting n- X failures . The mean of a binomial distribution is given by u = n.p Sles Or to od e nl The standard deviation of a binomial distribution is given by o = np(1 – p) 19). Construct the sample space for tossing a coin 20 times. Complete the following tasks: Let x = number of heads y co (8/ a). Construct a table consisting of Outcomes (x) versus Probability [P(x)] Use the table above to construct a histogram of the probability distribution. What do you notice? Use EXCEL to achieve this and include a hardcopy in your assignment. b). c). Determine the mean and standard deviation of the outcomes. d). How many standard deviations will most of the outcomes for 3 heads fall within?
Expert Answer:
Answer rating: 100% (QA)
20 a We have p probability of getting a head in a toss of a coin 05 so q 1p 05 np 2005 10 5 nq 2005 ... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
The following transactions occurred for Gullible Co. during the current year ended December 31. June 6: Reinstated the account of Ira Tate, which had been written off in the preceding year as...
-
a Evaluate the composite trapezium approximation with N=2 intervals for the integral [x In(x) sin(x)dx Type in the correct answer, with 2 d.p. (ex: 3.78) b Evaluate the composite trapezium...
-
Four balls are distributed between bucket 1 and bucket 2. Each step. a random ball is chosen, and moved to a different bucket. (a) Draw the directed graph (with arc-probabilities) describing the...
-
Can you describe the initialisation, exploration and exploitation phases of the cat hunting optimisation algorithm?
-
You have been given the following information about the production of Usher Co., and are asked to provide the plant manager with information for a meeting with the vice president of operations....
-
The Venn diagram in Fig. 4 shows the probabilities for its four basic regions. Find (a) Pr (E) (b) Pr (F) (c) Pr (E | F) (d) Pr (F | E). Figure 4 S E F
-
Defendant Monty J. Person began working for Garage Solutions, LLC, in March 2015. Three months into his employment, Person was sent by the owner of Garage Solutions, Mark Fontenot, to Rexburg, Idaho,...
-
Brecker Inc., a greeting card company, had the following statements prepared as of December 31, 2014. Additional information: 1. Dividends in the amount of $6,000 were declared and paid during 2014....
-
No Excel solution required Derive a formula that calculates the present value of an annuity that pays $1376 pa quarterly in perpetuity given an annual effective rate of interest of 3.7%. What is the...
-
Daniel Company uses a periodic inventory system. Data for 2015: beginning merchandise inventory (December 31, 2014), 2,000 units at $38; purchases, 8,000 units at $40; expenses (excluding income...
-
What types of positions in what types of industries might each of the eighteen inventories be used to assess? Explain the relationship between training and organizational development. How might each...
-
1 Express the extended fraction at the right as a simple 1 2+ fraction in lowest terms. 1 2+ 2+- 2
-
A company has the following capital structure: 1. Target weightings: 30% debt, 20% preferred stock,50%common equity 2. Tax rate 30% 3. The cost of debt 6.5% 4. Cost of preferred stock is 8% 5. The...
-
A commonly prescribed drug on the market for relieving nervous tension is believed to be only 60% effective. What is the probability that in a random sample of 100 adults, more than 70% (more than 70...
-
Find the sum of the terms in the arithmetic sequence below, Sn: 2, -2, -6, -10,..., -30 S = Sn (Simplify your answer.)
-
What factors should you consider when coming up with an OU design?
-
Sheffield corporation is considered the following alternatives: alternate a Alternate B revenues $ 44,000 $58,000 Variable costs 33,000 33,000 fixed costs 10,000 16,000 What is the incremental profit
-
Construct a 4 x 25 design confounded in two blocks of 16 observations each. Outline the analysis of variance for this design.
-
A wheel of radius 1.5 m rotates at a uniform speed. If a point on the rim of the wheel has a centripetal acceleration of 1.2 m/s2, what is the points tangential speed?
-
A beam of light in air is incident on the surface of a slab of fused quartz. Part of the beam is transmitted into the quartz at an angle of refraction of 30o relative to a normal to the surface, and...
-
If the billiard ball in Fig. 6.31 is in contact with the rail for 0.010 s, what is the magnitude of the average force exerted on the ball? 6060
-
Explain the difference between selling, general and administrative, and financial expenses.
-
What are the main types of accounts included in the Income statement to determine profit or loss? Define each.
-
State whether you think a business would recognise the following as revenue. When would it be recognised? a Cash sale by business $20 000 b Sale of excess equipment by a restaurant $350 c...
Study smarter with the SolutionInn App