Question

a population of values has a distribution with M= 106.3 and standards deviation =12.4 .you intended to draw a random sample of size.

what is the mean of the distribution of samples means?

what is the standard deviation of the distribution of the samples mean?

in a random sample of n =177, what is the probability that it's the random sample mean is more than 105.7 and less than 104.5

Answer 1

Solution :

Given that,

mean = = 106.3

standard deviation = = 12.4

n = 177

= = 106.3

= / n = 12.4 / 177 = 0.932

P(104.5< < 105.7)  

= P[(104.5 - 106.3) / 0.932 < ( - ) / < (105.7 - 106.3) / 0.932)]

= P( -1.93 < Z < -0.64)

= P(Z < -0.64) - P(Z < -1.93 )

Using z table,  

= 0.2611 - 0.0268

= 0.2343