Question

Suppose a random variable is normally distributed. The probabilities for a85 and 142 are 10% and 65%, respectively. Find the mean and standard deviation to the nearest whole number.

Answer 1

Mean (Expected Value):

$Mean (μ) = Σxp$

$Mean (μ) = (85\times0.10)+(142\times0.65)$

$Mean (μ) =8.50+92.30=100.80\approx101$

Standard Deviation (σ):

$\sigma=\sqrt{Σ(x-\mu)^{2} \rho}$

$\sigma=\sqrt{(85-101)^{2}\times0.1+(142-101)^2\times0.65}$

$\sigma=\sqrt{(256\times0.1)+(1681\times0.65)}$

$\sigma=\sqrt{25.6+168.1}$

$\sigma=\sqrt{193.7}$

$\sigma=13.9\approx14$