Without doing any computation, decide which has a higher probability, assuming e

Question

Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with

muequals=100

and

sigmaequals=15.

Explain your reasoning.

(a)

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=10

A.

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=20

has a higher probability. As n increases, the standard deviation decreases.

B.

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=20

has a higher probability. As n increases, the standard deviation increases.

C.

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=10

has a higher probability. As n increases, the standard deviation increases.

D.

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=10

has a higher probability. As n increases, the standard deviation decreases.

(b)

P(90less than or equalsx overbarxless than or equals110)

for a random sample of size

nequals=20

Explanation / Answer

AS THE DISTRIBUTION IS NORMAL

THE FORMULA TO BE USED = Z = (X-MEAN)/STANDARD DEVIATION

NOW THE CORRECT ANSWER WILL BE OPTION D

AS THE N = 10 AND AS THE N INCREASES THE STANDARD DEVIATION DECREASES HENCE OPTION D IS CORRECT

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