3. According to latest reported results of surveys administered by O'Reilly Media and Burtch Works, the median base salary of mid-level data scientists in the United States is $126,000, and 25% of such people earn less than $91,000. Assume that salaries follow a normal distribution.

(a) What is the probability that a randomly chosen data scientist earns less than $145,000 in salary?

(b) What is the probability that a randomly chosen data scientist earns more than $100,000 in salary?

(c) What is the probability that the average salary of a group of six randomly selected data scientists is between $110,000 and $150,000?

(d) Say we didn't assume that the salaries were normally distributed. According to available figures, 10% of data scientists earn less than $50,000 in salary, 15% earn more than $190,000, and 2% earn more than $290,000. Based on what you've been told, describe what you think the distribution of salaries looks like.