Answer: Mean = 0.40 and standard error = 0.0219 of the sampling distribution of sample proportions.
Step-by-step explanation:
Given : The proportion of community college students never use tutoring services available at their college: p= 0.40
Mean of the sampling distribution of sample proportions = p = 0.40
Since sample size : n= 500
Standard error = [tex]\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.40(1-0.40)}{500}}[/tex]
[tex]=\sqrt{\dfrac{0.24}{500}}[/tex]
[tex]=\sqrt{0.00048}=0.0219[/tex]
Hence, Mean = 0.40 and standard error = 0.0219 of the sampling distribution of sample proportions.