Question 1063045
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
:
high = 1 - P ( X < 120 )
z-score is ( 120 - 100 ) / 20 = 1
high = 1 - 0.8413 = 0.1587
:
medium = P ( X < 120 ) - P ( X < 70 )
medium = 0.8413 - 0.0668 = 0.7745
:
Use binomial distribution three times and then sum them
:
P ( k = 2 lows out of 10 ) = 10C2 * (0.0668)^2 * (1-0.0668)^(10-2) = 0.1155
:
P ( k = 5 mediums out of 10 ) = 10C2 * (0.7745^5) * (1-0.7745)^(10-5) = 0.0409
:
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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