3. Answer the following questions. (a) If a variable has a normal distribution w

Question

3. Answer the following questions.

(a) If a variable has a normal distribution with mean 5 and standard deviation 2, then what is the median of the variable?

(b) If a variable has a normal distribution with mean 5 and standard deviation 2, then what is the mode of the variable?

(c) Is the normal distribution symmetric around the mean, skewed to the left, or skewed to the right?

(d) Is the population proportion is always contained within a 95% confidence interval? 1

(e) If we take a very large number of samples of the same size from a population and calculate the 95% confidence interval for the proportion on each one of the samples, what percent will we expect to contain the population proportion?

Explanation / Answer

a) The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails. Normal distributions are defined by two parameters, the mean () and the standard deviation ().

So, median = 5

b) Mode = 5

c) Symmetric around mean

d) No, not always

e) 95%

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.