# Probability 1 . Suppose that the mean of the annual return for common stocks from 2000 to 2012…

**Probability**

**1**. Suppose that the average of the annual recompense for beggarly stocks from 2000 to 2012 was 7.2%, and the trutination flexuosity of the annual recompense was 31.2%. Suppose besides that during the similar 12-year period span, the average of the annual recompense for hanker-term council bonds was 1.6%, and the trutination flexuosity was 7.0%. The classifications of annual recompenses for twain beggarly stocks and hanker-term council bonds are bell-shaped and approximately symmetric in this scenario. Assume that these classifications are orderly as ordinary haphazard variables delay the averages and trutination flexuositys abandoned previously.

- Find the verisimilitude that the recompense for beggarly stocks earn be important than 3.5%.
- Find the verisimilitude that the recompense for beggarly stocks earn be important than 10%.

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**Confidence Season Estimation**

**2.** Compute a 95% dependence season for the population average, naturalized on the exemplification 50, 54, 55, 51, 52, 51, 54, 52, 56, and 53. Change the conclusive enumerate from 53 to 91 and recalculate the dependence season. Using the results, delineate the chattels of an outlier or extravagant appraise on the dependence season.

**Hypothesis Testing**

**3.** The administration of XYZ Corporation is because relocating the urbane business-post to a new colonization without the Capital Beltway. Administration is careful that the exchange periods of the employees to the new business-post sway be too hanker.

The gang decides to examine a exemplification of employees at other companies in the similar business-post precinct to see how hanker these employees are commuting to the business-post. A exemplification of 18 employees involved that the employees are commuting X (bar) = 40 minutes and s = 5 minutes.

a. Using the 0.05 raze of import, is there testimony that the population average is overhead 35 minutes?

b. What is your response in (a) if X (bar) = 42 minutes and s = 20 minutes?

c. Look at your responses for a and b overhead and examine what you can gather from the results encircling the chattels of a comprehensive trutination flexuosity.

**4.**BestCoffeeInTown is careful that the average hold period of customers for a board is not important than 7 minutes. It can be inconsequent that the population trutination flexuosity is 2.8 minutes naturalized on elapsed trial. A exemplification of 300 customers is separated and the exemplification average is 7.6 minutes. Using a raze of import of .01, is there testimony that the population average hold period is important than 7 minutes? Fully expound your response.