document.write( "Question 862354: Decide whether you can use the normal distribution to approximate the binomial distribution. 68% of children keep at least part of their savings in a saving account. You randomly select 50 children. Find the probability that at most 25 children will say yes. draw the respective graphs.\r
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Algebra.Com's Answer #519629 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "Hi
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document.write( "Note: We can use the normal distribution as a close approximation to the
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document.write( " binomial distribution whenever np ≥ 5 and nq ≥ 5.
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document.write( "can use the normal distribution to approximate the binomial distribution
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document.write( "Yes, 25.5 appropriate (did say at most, that is including 25) See generic examples below
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document.write( "m = .68*50 = 34  Sd = 3.2985   (\"sqrt%28.68%2A.32%2A50%29\"
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document.write( "z = (25.5-34)/3.2985= -2.58
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document.write( "P(z < -2.58) = .005\r
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document.write( "Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  
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document.write( "Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right
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document.write( "Examples Using the normal distribution to approximate binomial distribution probabilities with n = 50 and p = .4
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document.write( "a) exactly 18\r
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document.write( "Left endpoint for 18 is x=17.5\r
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document.write( "z-score for left endpoint 17.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 0.72, get .2642 
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document.write( "(2) if your z-table reads from the left, look up -0.72, get .2358\r
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document.write( "Right endpoint for 18 is x=18.5\r
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document.write( "z-score for right endpoint 18.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 0.43, get .1664 
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document.write( "(2) if your z-table reads from the left, look up -0.43, get .3336\r
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document.write( "(1) if your z-table reads from the middle, subtract .2642-.1664 = .0978  
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document.write( "(2) if your z-table reads from the left, subtract .3336-.2358 = .0978\r
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document.write( "Answer: .0978\r
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document.write( "b) anywhere from 21-25 including end points\r
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document.write( "Left endpoint for 21 is x=20.5\r
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document.write( "z-score for left endpoint 20.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 0.14, get .0557 
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document.write( "(2) if your z-table reads from the left, look up -0.72, get .5557\r
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document.write( "Right endpoint for 25 is x=25.5\r
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document.write( "z-score for right endpoint 25.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 1.59, get .4441 
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document.write( "(2) if your z-table reads from the left, look up 1.59, get .9441\r
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document.write( "(1) if your z-table reads from the middle, subtract .4441-.0557 = .3884  
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document.write( "(2) if your z-table reads from the left, subtract .9441-.5557 = .3884\r
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document.write( "Answer: .3884\r
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document.write( "c) more than 23\r
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document.write( "That means the smallest possible value is 24\r
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document.write( "Left endpoint for 24 is x=23.5\r
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document.write( "z-score for left endpoint 23.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 1.01, get .3438 
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document.write( "(2) if your z-table reads from the left, look up 1.01, get .8438\r
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document.write( "(1) if your z-table reads from the middle, subtract .5-.3438 = .1562
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document.write( "(2) if your z-table reads from the left, subtract 1-.8438 = .1562 
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document.write( "z-score for right endpoint 25.5 is \r
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document.write( "Answer: .1562\r
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document.write( "[Be careful here for part (d) coming up and other \"more than\" or \"at least\"
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document.write( "problems, if your table reads from the middle, then if the z-score is negative
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document.write( "you must ADD .5 not subtract. \r
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document.write( "d) at least 17\r
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document.write( "That means the smallest possible value is 17\r
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document.write( "Left endpoint for 17 is x=16.5\r
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document.write( "z-score for left endpoint 16.5 is \r
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document.write( "(1) if your z-table reads from the middle, look up 1.01, get .3438 
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document.write( "(2) if your z-table reads from the left, look up -1.01, get .1562\r
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document.write( "(1) if your z-table reads from the middle, add .5+.3438 = .8438,
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document.write( "because the z-score is negative.
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document.write( "(2) if your z-table reads from the left, subtract 1-.1562 = .8438  \r
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document.write( "Answer: .8438
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