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Suppose we select a simple random sample of size n=250 from a large population with a proportion p of successes. Let p be the proportion of successes in the sample. For which value of p is it appropriate to use the normal approximation for the sampling distribution of p?

A.0.03
B.0.15
C.0.02
D.0.97
E.0.99

Respuesta :

MathPhys

Answer:

B.0.15

Step-by-step explanation:

To approximate a binomial distribution as a normal distribution, two conditions must be met:

np > 10

nq = n (1−p) > 10

Here, n = 250.  Check each value of p to see if it meets the conditions.

A. p = 0.03

np = 7.5, nq = 242.5

B. p = 0.15

np = 37.5, nq = 212.5

C. p = 0.02

np = 5, nq = 245

D. p = 0.97

np = 242.5, nq = 7.5

E. p = 0.99

np = 247.5, nq = 2.5

Of the five choices, only B meets both conditions.

The correct option is B.0.15

  • The calculation is as follows;

To approximate a binomial distribution due to the normal distribution, two conditions must be fulfilled:

np > 10

nq = n (1−p) > 10

Here, n = 250.  

Now

B. p = 0.15

np = 37.5, nq = 212.5

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