Question

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

- If a random sample of size n = 49 is drawn, what is the
standard error (or standard deviation) of the sampling distribution

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

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

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

- 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

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