Question

Suppose a simple random sample of size n=41 is obtained from a population with mu=61 and sigma=19.

(b) Assuming the normal model can be​ used, determine

​P(x overbarx < 71.4).

​(c) Assuming the normal model can be​ used, determine

​P(x overbarx ≥ 69.1).

Answer 1

Solution :

Given that,

mean = = 61

standard deviation = = 19

n = 41

= = 61

a) = / n = 19 / 41 = 2.97

P( > 71.4) = 1 - P( < 71.4)

= 1 - P[( - ) / < (71.4 - 61) / 2.97]

= 1 - P(z < 3.50)

Using z table,    

= 1 - 0.9998

= 0.0002

b) P( 69.1 ) = P(( - ) / (69.1 - 61) / 2.97 )

= P(z 2.72)

Using z table

= 0.9967