Question

Suppose x has a distribution with μ = 12 and σ = 9.

A.) If a random sample of size n = 35 is drawn, find μ_x, σ_x and P(12 ≤ x ≤ 14). (Round σ_x to two decimal places and the probability to three decimal places.)

P(12 ≤ x ≤ 14)=

B.) If a random sample of size n = 62 is drawn, find μ_x, σ_x and P(12 ≤ x ≤ 14). (Round σ_x to two decimal places and the probability to three decimal places.)

P(12 ≤ x ≤ 14)=

Answer 1

Solution :

Given that ,

mean = μ = 12

standard deviation = = 9

n = 35

= 12

=  / n= 9/ 35=1.52

P(12 ≤ x ≤ 14)= = P[(12-12) /1.52 < ( - ) /   < (14-12) /1.52 )]

= P( 0< Z <1.32 )

= P(Z <1.32 ) - P(Z < 0)

Using z table

=0.9066-0.5

=0.4066

probability= 0.4066

b.

mean = μ = 12

standard deviation = = 9

n = 62

= 12

=  / n= 9/ 62=1.14

P(12 ≤ x ≤ 14)= = P[(12-12) /1.14 < ( - ) /   < (14-12) /1.14 )]

= P( 0< Z <1.75 )

= P(Z <1.75 ) - P(Z < 0)

Using z table

=0.9599-0.5

=0.4599

probability= 0.4599