Question

Suppose x has a distribution with μ = 17 and σ = 13.

(a) If a random sample of size n = 42 is drawn, find μ_x, σ_x and P(17 ≤ x ≤ 19). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(17 ≤ x ≤ 19) =

(b) If a random sample of size n = 67 is drawn, find μ_x, σ_x and P(17 ≤ x ≤ 19). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(17 ≤ x ≤ 19) =

Answer 1

Solution :

Given that,

mean = = 17

standard deviation = = 13

a) n = 42

= = 17

= / n = 13 / 42 = 2.01

P( 17 19 )  

= P[(17 - 17) / 2.01 ( - ) / (19 - 17) / 2.01)]

= P(0 Z 1.00)

= P(Z 1.00 ) - P(Z 0)

Using z table,  

= 0.8413 - 0.5

=  0.3413

b) n = 67

= = 17

= / n = 13 / 67 = 1.59

P( 17 19 )  

= P[(17 - 17) / 1.59 ( - ) / (19 - 17) / 1.59)]

= P(0 Z 1.26)

= P(Z 1.26 ) - P(Z 0)

Using z table,  

= 0.8962 - 0.5

=  0.3962