? asked in Science & MathematicsMathematics · 8 years ago

Estimation & The CLT?

The heights of boys at sixth form college are assumed to be normally distributed wit ha mean of 162cm and a standard deviation of 3.5cm.

a) If a sixth form boy is selected at randome what is the probability that his height is greater than 163cm?

b) A sixth form set has 10 boys. Calculate the probability that the mean height of the boys in the set is greater than 163cm.

c) What is the probability that all 10 boys have heights greater than 163cm?

1 Answer

Relevance
  • cidyah
    Lv 7
    8 years ago
    Best Answer

    a)

    μ = 162

    σ = 3.5

    standardize x to z = (x - μ) / σ

    P(x > 163) = P( z > (163-162) / 3.5)

    = P(z > 0.2857) = .3859

    (From Normal probability table)

    b)

    Mean μ = 162

    Standard deviation σ = 3.5

    Standard error σ / √ n = 3.5 / √ 10 = 1.1067972

    standardize xbar to z = (xbar - μ) / (σ / √ n )

    P(xbar > 163) = P( z > (163-162) / 1.106797)

    = P(z > 0.9035) = .1841

    (from normal probability table)

    c)

    From (a) , for one boy, the probability is .3859

    For all 10 boys , the probability of height > 163cm = (.3859)^10 = .0000732

Still have questions? Get your answers by asking now.