1 Suppose that samples of n 25 are selected at random from

1. Suppose that samples of n = 25 are selected at random from a normal population with mean loo and standard deviation 10. What Is the probability that the sample mean falls in the interval from Mug - l.8sigmag to Mug + 1.0 sigmag:? (Mux: sample mean: sigmax : sample standard deviation) (3)

Solution

Given that x bar = 100

s = 25

n = 25

Sigma = std error = 25/rt 25 = 5

mu =100

Thus the interval is {100-5(1.8), 100+5(1)}

= (91, 106)

Prob for (91,106) = P(-1.8<Z<1) = 0.4641+0.3414

= 0.8055