Question

Suppose x has a distribution with μ = 31 and σ = 15.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

(c) Find P(27 ≤ x ≤ 32). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean =   = 31

standard deviation = = 15   

n = 16

= 31

=  / n= 15 / 16=3.75

  P(27 ≤ x ≤ 32) = P[(27-31) /3.75 < ( - ) /   < (32-31) / 3.75)]

= P( -1.07< Z < 0.27)

= P(Z <0.27 ) - P(Z <-1.07 )

Using z table

=0.6064-0.1423

=0.4641

probability=0.4641