Question

Suppose x has a distribution with μ = 27 and σ = 23.

(a) If a random sample of size n = 39 is drawn, find μ_x, σ_x and P(27 ≤ x ≤ 29).

μx =

σx =

P(27 ≤ x ≤ 29) =

(b) If a random sample of size n = 62 is drawn, find μ_x, σ_x and P(27 ≤ x ≤ 29).

μx =

σx =

P(27 ≤ x ≤ 29) =

Answer 1

Solution :

Given that ,

mean =   = 27

standard deviation = = 23   

n = 39

= 27

=  / n= 23 / 39=3.68

P(27 ≤ x ≤ 29) = = P[(27-27) /3.68 < ( - ) /   < (29-27) /3.68 )]

= P( 0< Z < 0.54)

= P(Z <0.54 ) - P(Z <0 )

Using z table

=0.7054 - 0.5000

=0.2054

probability= 0.2054

b

n = 62

= 27

=  / n= 23 / 62=2.92

P(27 ≤ x ≤ 29) = = P[(27-27) /2.92 < ( - ) /   < (29-27) /2.92)]

= P( 0< Z < 0.68)

= P(Z <0.68 ) - P(Z <0 )

Using z table

=0.7517- 0.5000

=0.2517

probability= 0.2517