Question

3) Fill in the blank. Suppose you have a normal distribution N(6,2), i.e. μ=6, σ = 2 (10 pts) ~68% of observations will fall between _____ and _____ .
(10 pts) ~2.5% of observations will fall below _____ .
(10 pts) ~0.15% of observations will fall above ______.

Answer 1

Solution :

Given that,

= 6

= 2

Using Empirical rule,

P( - 1< X < + 1) = 68%

P(6 - 1 * 2 < X < 6 + 1 * 2) = 68%

P(6 - 2 < X < 6 + 2) = 68%

P(4 < X < 8) = 68%

68% of observations will fall between 4 and 8 .

2.5% of observations will fall below = 6 - 2 * 2 = 2

2.5% of observations will fall below = 2

0.15% of observations will fall above = 6 - 3 * 2 = 0

2.5% of observations will fall below 0