A hormal distribution (continuous curve and bell shaped) can be used to approximate a binomial distribution...

  

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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?

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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