a What are the characteristics of the standard normal distri

(a) What are the characteristics of the standard normal distribution? (b) The HR department of an organization collects data on employees\' age, salary, level of education, gender, and ethnicity. Which data do you think is more likely to follow a normal distribution? Explain why.

Solution

(a) What are the characteristics of the standard normal distribution?

The standard normal distribution is the normal distribution with a mean of zero (m = 0) and a variance of one (s^2 = 1).

(i) The distribution is bell shaped

(ii) The normal probability density function is symmetric about its mean value

(iii) The mean, median and mode of the distribution coincide (all are 0)

(iv) The inflection points of the curve occur at one standard deviation away from the mean.

(b) The HR department of an organization collects data on employees\' age, salary, level of education, gender, and ethnicity. Which data do you think is more likely to follow a normal distribution? Explain why.

Age follows a normal distribution because it measures in continuous scale.

Salary does not follows normal distribution because it is not bell shaped distribution. Salaries of manager are high, the distribution is skewed.

level of education, gender, and ethnicity are not normal because they are categorical variable.