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The scores on a national achievement test are normally distributed with a mean of 50 and a standard deviation of 10. Out of a group of 200 students, how many would you expect to score more than 70?

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    μ=50, σ=10;
    For score 70, convert to standardized value
    z=(x-μ)/σ=(70-50)/10=2
    P(x>70)=P(z>2)
    Look up standard normal distribution table to get
    P(z<=2)=0.9772, so
    P(x>70)=P(z>2)=1-0.9772=0.0228
    or the average number of students with score of 70 or more
    = P(x>70)*200=4.56 = 5 approx.

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