Question

you draw a marble from a bag of numbered marbles whose numbers are normally distributed for some reason. your marble is labeled '27', and because you're psychic, you know that the mean of the numbered marbles is '21' and also that 43.32% of the marbles are between 21 and 27. What is the standard deviation of the bag of marble numbers? (the answer is an integer)

Answer 1

Let's denote X as the numbered marbles.

P(21≤ X ≤27) = 0.4332

$\frac{P(21-21)}{\sigma_{x}}\leq \frac{X-21}{\sigma_{x}}\leq \frac{27-21}{\sigma_{x}}$

P( 0 ≤ z ≤ 6/σx) = 0.4332; Z is the z-score here

1.5 = 6/σx

σx = 4