Step 1

Central Limit Theorem (CLT): - If \(X\sim N(\mu,\sigma)\) and sample size n are very large then the sample mean also follows a normal distribution.

Step 2

1) For the proportion, if np >10 and nq> 10 and the sample size is large then it follows the normal distribution. So, this is not correct.

2)CLT specifies the specific mean of the curve which approximates certain sampling distributions is true.

4) CLT specifies the specific standard deviation of the curve which approximates certain sampling distributions is correct.

5)Its name is often abbreviated by the three capital letters CLT is correct.

6)The accuracy of the approximation it provides, improves as the sample size n increases is correct.

8) CLT specifies the specific shape of the curve which approximates certain sampling distributions is correct.

Central Limit Theorem (CLT): - If \(X\sim N(\mu,\sigma)\) and sample size n are very large then the sample mean also follows a normal distribution.

Step 2

1) For the proportion, if np >10 and nq> 10 and the sample size is large then it follows the normal distribution. So, this is not correct.

2)CLT specifies the specific mean of the curve which approximates certain sampling distributions is true.

4) CLT specifies the specific standard deviation of the curve which approximates certain sampling distributions is correct.

5)Its name is often abbreviated by the three capital letters CLT is correct.

6)The accuracy of the approximation it provides, improves as the sample size n increases is correct.

8) CLT specifies the specific shape of the curve which approximates certain sampling distributions is correct.