According to Glassdoor, the average base salary for a brand manager in Bethlehem, PA$,$ is $$88,592$ and the average base salary for a brand manager in New York City, NY is $$97,417.$ Assume that salaries are normally distributed, the standard deviation for brand managers in Bethlehem is $$19,000,$ and the standard deviation for brand managers in New York is $$21,000.$

a$.$ What is the probability that a brand manager in Bethlehem has a base salary in excess of $$100,000?$

b$.$ What is the probability that a brand manager in New York has a base salary in excess of $$100,000?$

c$.$ What is the probability that a brand manager in New York has a base salary of less than $$75,000?$

d$.$ How much would a brand manager in New York have to make in order to have a higher salary than $99\%$ of the brand managers in Bethlehem $($do not use neither the dollar sign nor coma in your answer$)?$ $