Question

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 1

Mean = 14.5 years and standard deviation = 0.34 years

Explanation:

Data provided in the question:

Mean of the normal distribution = 14.5 years

Population standard deviation, σ = 2.5 years

Sample size = 55 students

Now,

The mean of the sample of 55 students will remain the same i.e 14.5 years

and,

Standard deviation of the sample of 55 students will be calculated using the formula

=
`(\sigma)/(√(n))`

here n is the sample size

thus,

Standard deviation of the sample of 55 students, σₓ =
`(2.5)/(√(55))`

= 0.337 ≈ 0.34

Hence,

the Mean = 14.5 years and standard deviation = 0.34 years