A population has a mean of 50 and a standard deviation of 19. If a random sample

A population has a mean of 50 and a standard deviation of 19. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following?

a. Greater than 56
b. Less than 54
c. Less than 52
d. Between 47.5 and 53.5
e. Between 50.9 and 51.5

Here X~Normal(50,19)

As a random sample of 64 is taken so the sample mean,

Sample mean ~Normal(50,= Normal(50, 19/8)

a)    P(mean > 56) = 1-P(Mean<56) = 1- = 1- P(Z< 2.53) =1-0.9943 = ____________________

b)    P(Mean < 54) =  = P(Z< 1.68) = ____________________

c)    P(Mean < 52) =  = P(Z<0.84) = ____________________

d)    P(47.5< Mean < 53.5) = P(Mean<53.5) – P(Mean<47.5)

=

= P(Z<1.47) – P(Z< -1.05)

= 0.9292 – 0.1469 = ____________________

e)    P(50.9< Mean < 51.5) = P(Mean<51.5) – P(Mean<50.9)

=

= P(Z<0.63) – P(Z< 0.38)

= 0.7357-0.6480 = ____________________