Probability Problems

1. The average starting salary for this year’s graduates at a large university is $30,000 with a standard deviation of $8,000.
a. What is the probability that a random selected graduate will have a starting salary of at least $40,400?
b. Individuals with starting salaries of less than $21,600 receive a low income tax break. What % of the graduates will receive the tax break?
c. What are the minimum and maximum starting salaries of the middle 95% of the graduates?
d. If 189 of the recent graduates have salaries of at least $42,240, how many students graduated this year from this university?

2. The price of a stock is uniformly distributed between $30 and $40
a. What is the probability that the stock price will be between $34 and $38?
b. What is the probability that the stock price will be less than or equal to $32?
c. What is the expected price of the stock?
d. What is the variance?

3. A new soft drink is being market tested. It is estimated that 60% of the consumers will like the new drink. A sample of 96 taste tested the new drink.
a. What are the expected value, standard deviation, and shape of the sampling distribution?
b. What is the probability that more than 70.4% of consumers will indicate they like the drink?
c. What is the probability that between 55% and 65% will indicate they like the new drink?

4. A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The standard deviation is known to be $60.
a. What is the 90% confidence interval of the population mean?
b. What size sample should be selected to obtain a 0.90 probability of estimating the average daily balance within $5 or less?

5. Bastien, Inc. has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 6 miles per gallon.
a. With a 0.05 level of significance, test to determine whether or not the manufacturer’s advertising campaign is legitimate. (Must state the null and alternative hypothesis, the rejection rule, the test statistic, the conclusion, and interpretation.)

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