Question

a) Given X ~N(10, 18)  and n = 64

P(13 < X < 14) =

b)

Given X ~N(10, 18)  and n = 64

x-bar ~ N(10, _________)

c) Given X ~N(10, 18)  and n = 64

μ = _____

Answer 1

Solution :

Given that,

mean = = 10

standard deviation = = 18

n = 64

= = 10

= / n = 18/ 64 = 2.25

a)

P(13 < < 14) = P((13 - 10) /2.25 <( - ) / < (14 - 10) /2.25 ))

= P(1.33 < Z < 1.78)

= P(Z < 1.78) - P(Z < 1.33) Using z table,

= 0.9625 - 0.9082

= 0.0543

b)

X N(10, 18)  and n = 64

= / n = 18/ 64 = 2.25

x bar N ( 10 , 2.25 )

c)

Given X N(10, 18)  and n = 64

= 10