Question

A population of values has a normal distribution with μ = 174.2 μ = 174.2 and σ = 45.8 σ = 45.8 . You intend to draw a random sample of size n = 48 n = 48 .

Find the probability that a sample of size n = 48 n = 48 is randomly selected with a mean greater than 187.4. P( ¯¯¯ X X ¯ > 187.4) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

= 174.2

= / n = 45.8 / 48 = 6.61

P( > 187.4) = 1 - P( < 187.4)

= 1 - P[( - ) / < (187.4 - 174.2) / 6.61]

= 1 - P(z < 2.00)   

= 1 - 0.9772

= 0.0228