Question

Suppose a simple random sample of size n=64 is obtained from a population with μ=76 and σ=8.

​(a) Describe the sampling distribution of x̅

​(b) What is P (x̅ > 77.7)?

​(c) What is P (x̅ ≤ 73.65)?

​(d) What is P (74.5 < x̅ < 78.15)?

Answer 1

Solution :

(a)

= 76

= / n = 8 / 64 = 1

(b)

P( > 77.7) = 1 - P( < 77.7)

= 1 - P[( - ) / < (77.7 - 76) / 1]

= 1 - P(z < 1.7)

= 0.0446

(c)

P( 73.65) = P(( - ) / (73.65 - 76) / 1)

= P(z -3.35)  

= 0.0004

(d)

= P[(74.5 - 76) / 1 < ( - ) / < (78.15 - 76) / 1)]

= P(-1.5 < Z < 2.15)

= P(Z < 2.15) - P(Z < -1.5)

= 0.9842 - 0.0668

= 0.9174