Question

Suppose x has a distribution with μ = 18 and σ = 17.

(a) If a random sample of size n = 33 is drawn, find μx, σ x and P(18 ≤ x ≤ 20). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(18 ≤ x ≤ 20) =

(b) If a random sample of size n = 61 is drawn, find μx, σ x and P(18 ≤ x ≤ 20). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(18 ≤ x ≤ 20) =

Answer 1

Solution :

Given that ,

mean =   = 18

standard deviation = = 17

n = 33

= 18

=  / n= 17/ 33=2.96

P(18 ≤ x ≤ 20) = P[(18 -18) /2.96 < ( - ) /   <(20-18) /2.96)]

= P( 0< Z <0.68 )

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

Using z table

=0.7517 -0.5

=0.2517

probability= 0.2517

b.

n = 61

= 18

=  / n= 17/ 61=2.18

P(18 ≤ x ≤ 20) = P[(18 -18) /2.18 < ( - ) /   <(20-18) /2.18)]

= P( 0< Z <0.92)

= P(Z <0.92 ) - P(Z <0 )

Using z table

=0.8212 -0.5

=0.3212

probability= 0.3212