Question

Suppose x has a distribution with μ = 16 and σ = 10.

(a) If a random sample of size n = 45 is drawn, find μx, σ x and P(16 ≤ x ≤ 18). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(16 ≤ x ≤ 18) =

(b) If a random sample of size n = 72 is drawn, find μx, σ x and P(16 ≤ x ≤ 18). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(16 ≤ x ≤ 18) =

Answer 1

Part a.

n=45

P( 16 < X < 18)

X1= 16   , X2 = 18

Using Z formula ,

Z = 0

Z =1.34

P( 16< X < 18) = P(0 < Z<1.34) = P(Z<1.34) - P(Z<0) = 0.9099-0.5 =0.4099

( using Z table we check for 1.34 check , 1.3 row and 0.04 column we get 0.9099 for 0 in table we get 0.5)

Part b.

n = 72

P( 16 < X < 18)

X1= 16   , X2 = 18

Using Z formula ,

Z = 0

Z =1.70

P( 16< X < 18) = P(0 < Z<1.70) = P(Z<1.70) - P(Z<0) = 0.9554-0.5 =0.4554

( using Z table we check for 1.70 check , 1.7 row and 0.00 column we get 0.9554 for 0 in table we get 0.5)