suppose a random sample of size n 49 is obtained from a pop

suppose a random sample of size n = 49 is obtained from a population with u=73 and 0=28.

Suppose a simple random sample of size n= 49 is obtained from a population with mu= 73 and sigma= 28. (1 (a) Describe the sampling distribution of x. g @)What is P (c) What is P ? (d) What is p (67.4

Solution

Answer

a).   B the distribution is approximately normal ( because n>30)

mean =73

SD=28/sqrt(49) = 4

b).

z value for 80.6, z=(80.6-73)/4 =1.9

P( meanx >80.6) = P(z > 1.9) = 0.0287

c).

z value for 63.6, z=(63.6-73)/4 = -2.35

P( meanx <= 63.6) = P(z <= -2.35) = 0.0094

z value for 79, z=(79-73)/4 = 1.5

z value for 67.4, z=(67.4-73)/4 = -1.4

P(67.4< meanx<79) = P(-1.4<z<1.5) = 0.9332 - 0.0808 = 0.8524