Question 1063045: Help pls. suppose an individual's scores on repetitions of a certain task are independently and normally distributed with mean 100 and standard deviation 20. a score is said to be low if it is below 70, high if it is above 120, and medium if it is between 70 and 120. determine the probability that the individual scores two lows, five mediums, and three highs in ten repetitions of the task.thanks!
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Use z-score and z-tables to calculate probabilities
:
low = P ( X < 70 )
z-score is (70 - 100) / 20 = -1.5
P ( X < 70 ) = 0.0668
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high = 1 - P ( X < 120 )
z-score is ( 120 - 100 ) / 20 = 1
high = 1 - 0.8413 = 0.1587
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medium = P ( X < 120 ) - P ( X < 70 )
medium = 0.8413 - 0.0668 = 0.7745
:
Use binomial distribution three times and then sum them
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P ( k = 2 lows out of 10 ) = 10C2 * (0.0668)^2 * (1-0.0668)^(10-2) = 0.1155
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P ( k = 5 mediums out of 10 ) = 10C2 * (0.7745^5) * (1-0.7745)^(10-5) = 0.0409
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P ( k = 3 highs out of 10 ) = 10C3 * (0.1587)^3 * (1-0.1587)^(10-3) = 0.1431
:
0.1155 + 0.0409 + 0.1431 = 0.2995
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probability that the individual scores two lows, five mediums, and three highs in ten repetitions is approximately 0.2995
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