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# Given a data set find various probabilities and construct confidence intervals.

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The average weekly earnings for women in managerial and professional positions is \$685 with a standard deviation of \$45. Salaries are normally distributed. Answer the following questions.

a. What is the probability that a woman will have a weekly salary of more than \$650?
b. What is the probability that a woman will have a weekly salary of at least \$800?
c. For the population, in what range does the middle 95% of weekly salaries lie?
d. If a new sample of 40 women is selected, what is the probability that the mean weekly salary will be between \$670 and \$705?
e. If new samples of 50 families are selected, what weekly salary to the nearest dollar marks the top 10% of the means of these new samples?
f. If new samples of 100 women are selected, what range of weekly salaries to the nearest dollar marks the 98% confidence interval?