The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i

Discussion in 'Calculator Requests' started by math_celebrity, Jan 8, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

    a) What is the probability that a randomly person has an IQ between 85 and 115?
    b) Find the 90th percentile of the IQ distribution
    c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

    a) 68% from the empirical rule calculator
    b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)<br />
    (X - 100)/10 = 1.21852
    X = 113 rounded up
    c) Sample standard deviation is the population standard deviation divided by the square root of the sample size
    15/sqrt(100) = 15/10 = 1.5

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