A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below. ssions = 0.05 years o = 2.5 years 0; = 0.34 years Thread Store OH = 14.5 years

Answer:The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.Step-by-step explanation:The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Population:[tex]\mu = 14.5, \sigma = 2.5[/tex]Sample:55 students, so [tex]n = 55[/tex]Then[tex]\mu = 55, s = \frac{2.5}{\sqrt{55}} = 0.34[/tex]The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.