Test 3 Question 4 Answer

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Test 3

4.  Suppose a simple random sample of size n=150 is obtained from a population whose size is N=15,000 and whose population proportion with a specified characteristic is p=0.4. Complete parts ​(a) through​ (c) below.

 

​(a) Describe the sampling distribution of .

Choose the phrase that best describes the shape of the sampling distribution below.

  1. Not normal because n≤0.05N and np(1−p)<10.
  2. Not normal because n≤0.05N and np(1−p)≥10.
  3. Approximately normal because n≤0.05N and np(1−p)≥10.
  4. Approximately normal because n≤0.05N and np(1−p)<10.

Determine the mean of the sampling distribution of .

Determine the standard deviation of the sampling distribution of

.

(b) What is the probability of obtaining x or more individuals with the​ characteristic? That​ is, what is ​P(​)?

(c) What is the probability of obtaining x or fewer individuals with the​ characteristic? That​ is, what is ​P(​)?

 

 

 

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This question is taken from Math 136 – Introduction to Statistics » Summer 2021 » Test 3