Question

1. Suppose x has a distribution with µ = 15 and σ = 14
   1. If a random sample of size n = 49 is drawn, what is the standard error (or standard deviation) of the sampling distribution x?

2. Find P (15 < x < 17) for a random sample of size n = 49.

3. If a random sample of size n = 64 is drawn, what is the standard error of the x sampling distribution?

4. Find P (15 < x < 17) for a random sample of size n = 64.      

5. Compare the probabilities found in b and d. Why is one larger than the other one?

Answer 1

Solution :

Given that,

mean = = 15

standard deviation = = 14

n = 49

a) = = 15

= / n = 14 / 49 = 2

b) P(15 < < 17)  

= P[(15 - 15) / 2 < ( - ) / < (17 - 15) / 2)]

= P( 0 < Z < 1.0)

= P(Z <1.0 ) - P(Z <0 )

Using z table,  

= 0.8413 - 0.5  

= 0.3413

n = 64

c) = = 15

= / n = 14 / 64 = 1.75

d) P(15 < < 17)  

= P[(15 - 15) / 1.75 < ( - ) / < (17 - 15) / 1.75)]

= P( 0 < Z < 1.14)

= P(Z <1.14 ) - P(Z <0 )

Using z table,  

= 0.8729 - 0.5  

= 0.3729

e) A probability of part (d) is larger than part (b) , because part (d) sample size larger, standar error is smaller