Question

Suppose x has a distribution with μ = 11 and σ = 10.

(a) If a random sample of size n = 36 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(11 ≤ x ≤ 13) =

(b) If a random sample of size n = 64 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(11 ≤ x ≤ 13) =

Answer 1

Solution :

Given that,

mean = = 11

standard deviation = = 10

a) n = 36

= = 11

= / n = 10 / 36 = 1.67

P(11 13)  

= P[(11 - 11) /1.67 ( - ) / (13 - 11) / 1.67)]

= P(0 Z 1.20)

= P(Z 1.20) - P(Z 0)

Using z table,  

= 0.8849 - 0.5

= 0.3849

b) n = 64

= = 11

= / n = 10 / 64 = 1.25

P( 11 13)  

= P[(11 - 11) /1.25 ( - ) / (13 - 11) / 1.25)]

= P(0 Z 1.60)

= P(Z 1.60) - P(Z 0)

Using z table,  

= 0.9452 - 0.5

= 0.4452