1. The probability that a manager who makes business transactions in a foreign language is 0.2. Ten (10) managers are chosen randomly.

a) What is the probability that none make commercial transactions foreign language?

b) What is the probability that at least 2 do?

c) What is the probability that the 10 do? d) Graph the probability distribution and discuss its shape.

Use Megastat to corroborate your answers.

2. BusinessWeek surveyed students who finished their 30 studies in a master's program (BusinessWeek, September 22 2003). According to this survey, the average annual salary of a woman and a man 10 years after completing their studies is $ 117.000 and $ 168.000, respectively. Consider these amounts as means populations of wages of a woman and a man. Suppose the population standard deviation between the wages of women is $ 25,000 and between the wages of men is $ 40,000. With this information:

a) What is the probability that a simple random sample of 40 men the sample mean does not differ more than $ 10,000 average Population of $ 168.000?

b) What is the probability that a simple random sample of 40 the sample mean women do not differ more than $ 10,000 average Population of $ 117.000?

c) Which of the two cases a) and b) are more likely to get a sample mean not differ by more than $ 10,000 from the population mean? Why?

d) What is the probability that a simple random sample of 100 men, the sample mean does not differ by more than $ 4,000 average Population?

Note: since the size of populations is not known assume they are endless.