The average base salary for women working as copywriters in advertising firms is

Question

The average base salary for women working as copywriters in advertising firms is higher than the average base salary fro men. The average base salary for women is $67,000 and the average base salary for men is $65,500. Assume salaries are normally distributed and that the standard deviation is $7000 for both men and women.

- What is the probability of a woman receiving a salary in excess of $75,000 ?

- What is the probability of a man receiving a salary in excess of $75,000 ?

- What is the probability of a woman receiving a salary below $50,000 ?

- How much would a woman have to make to have a higher salary than 99% of her male counterparts ?

Explanation / Answer

Given women: X~Normal(mean=67000, s=7000) Men: Y~Normal(mean=65500, s=7000) - What is the probability of a woman receiving a salary in excess of $75,000 ? P(X>75000) =P((X-mean)/s > (75000-67000)/7000) =P(Z> 1.14) = 0.1271(check standard normal table) - What is the probability of a man receiving a salary in excess of $75,000 ? P(Y>75000) =P((Y-mean)/s > (75000-65500)/7000) =P(Z> 1.36) = 0.0869(check standard normal table) - What is the probability of a woman receiving a salary below $50,000 ? P(X c =65500 +2.33*7000 =81810

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