Question # Suppose the ages of students in Statistics 101 follow a normal distribution with a mean of 23 years and a standard deviation of 3 years

Normal distributions
ANSWERED Suppose the ages of students in Statistics 101 follow a normal distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect.
A) The expected value of the sample mean is equal to the population’s mean.
B) The standard deviation of the sampling distribution is equal to 3 years.
C) The shape of the sampling distribution is approximately normal.
D) The standard error of the sampling distribution is equal to 0.3 years. 2021-09-13
Solution :
Given that ,
mean $$\displaystyle=\mu={23}$$
standard deviation $$\displaystyle=\sigma={3}$$
The shape of the sampling distribution is approximately normal n = 100
$$\displaystyle\mu_{{\overline{{{x}}}}}=\mu={23}$$ and
$$\displaystyle\sigma_{{\overline{{{x}}}}}={\frac{{\sigma}}{{\sqrt{{{n}}}}}}={\frac{{{3}}}{{\sqrt{{{100}}}}}}={0.3}$$
The incorrect statement is,
The standard deviation of the sampling distribution is equal to 3 years.
Option B) is correct.