Question

Suppose x has a distribution with μ = 30 and σ = 23.

(a) If a random sample of size n = 42 is drawn, find μ_x, σ_x and P(30 ≤ x ≤ 32). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(30 ≤ x ≤ 32) =

(b) If a random sample of size n = 70 is drawn, find μ_x, σ_x and P(30 ≤ x ≤ 32). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(30 ≤ x ≤ 32) =

Answer 1

Solution :

Given that,

mean = = 30

standard deviation = = 23

a ) n = 42

= 30

₌ / n =  23 42 = 3.5490

P (30     x   32 )

P ( 30 - 30 / 3.5490)    ( - /   ) < ( 32 - 30 / 3.5490)

P ( 0 / 3.5490    z   2 / 3.5490 )

P (0 < z < 0.56)

P ( z   0.56 ) - P ( z   0 )

Using z table

= 0.7123 - 0.5000

= 0.2123

Probability = 0.2123

b ) n = 70

= 30

₌ / n =  23 70 = 2.7490

P (30     x   32 )

P ( 30 - 30 / 2.7490)    ( - /   ) < ( 32 - 30 / 2.7490)

P ( 0 / 2.7490    z   2 / 2.7490 )

P (0 < z < 0.73 )

P ( z   0.73 ) - P ( z   0 )

Using z table

= 0.7673 - 0.5000

= 0.2673

Probability = 0.2673