Question

A population's distribution is normal with a mean of 18 and standard deviation of 4. A sample of 16 observations is selected and a sample mean computed. What is the probability that the sample mean is more than 18?

Answer 1

Solution :

Given that ,

mean = = 18

standard deviation = = 4

n = 16

= 18

= / n = 4 / 18 = 1

P( >18 ) = 1 - P( <18 )

= 1 - P[( - ) / < (18-18) / 1]

= 1 - P(z <0 )

Using z table

= 1 - 0.5

= 0.5

probability= 0.5