Question

A simple random sample of size n=36 is obtained from a population that is skewed right with μ=74 and σ=24.

​(a) Describe the sampling distribution of overbarx.

​(b) What is P ( x overbar > 80.6 )​?

​(c) What is P (x overbar ≤64.6​)?

​(d) What is P ( 70<x<80​?)

​(a) Choose the correct description of the shape of the sampling distribution of overbarx.

A.The distribution is skewed left.

B.The distribution is uniform.

C.The distribution is approximately normal.

D.The distribution is skewed right.

E.The shape of the distribution is unknown.

Answer 1

Solution :

Given that ,

mean = = 74

standard deviation = = 24

n = 36

(a)

The distribution is approximately normal

= 74

= / n = 24 / 36 = 4

(b)

P( > 80.6) = 1 - P( < 80.6)

= 1 - P[( - ) / < (80.6 - 74) / 4]

= 1 - P(z < 1.65)

= 0.0495

(c)

P( 64.6) = P(( - ) / (64.6 - 74) / 4)

= P(z -2.35)

= 0.0094

(d)

= P[(70 - 74) / 4< ( - ) / < (80 - 74) / 4)]

= P(-1 < Z < 1.5)

= P(Z < 1.5) - P(Z < -1)

= 0.9332 - 0.1587

= 0.7745