Question

Suppose you have a normal distribution with known mu = 11 and sigma = 5. N(11,5). Using the 68,95,99.7 rule, what is the approximate probability that a value drawn from this distribution will be:

a.Between 6 and 16?

b.Between 1 and 21?

c.Greater than 16?

d.Less than 1?

e.Less than 21?

Answer 1

Solution :

Given that,

Using Empirical rule,

(a)

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

P(11 - 5 < X < 11 + 5) = 68%

P(6 < X < 16) = 68%

68%

(b)

P( - 2< X < + 2) = 95%

P(11 - 2 * 5 < X < 11 + 2 *5) = 95%

P(1 < X < 21) = 95%

95%

(c)

P(X > 16) = 16%

(d)

P(X < 1) = 0.025 = 2.5%

(d)

P(X < 21) = 97.5%