*For each component, include a labelled sketch of the curve, a list of the variables given/calculated, and a list of any formulas used, along with the rounded answer(s). You may use Excel functions and formulas to obtain your values, or algebra and the appropriate table.

PART A Probabilities using the Normal Distribution

1. The average monthly cost for utilities (for a 4-bedroom house) has been quoted at $426 with a standard deviation of $81.22.
2. What is the probability that a random household is chosen and the monthly utilities costs are between $329 and $459?
3. What is the probability that a sample of 20 houses has a monthly utilities bill of over $475?
4. What is the monthly utilities cost for a home that is located at the first quartile of the data?

PART B Confidence Interval Estimate of Mean, unknown

1. Data representing annual earnings by a group of professionals is listed below:

$134,755 $120,000 $135,000 $111,511 $108,869 $96,235

$121,795 $129,007 $111,766 $110,884 $117,469 $114,134

$129,295 $136,134 $101,088 $148,625 $142,080 $105,594

$163,788 $133,488 $144,500 $83,970 $106,150 $125,784

$101,922 $99,504 $106,557 $95,783 $118,787 $113,000

1. Determine the sample mean and sample standard deviation. *Do not round these values as you use them in further steps.*
2. Calculate the 98% confidence interval estimate of the true population mean for annual earnings by this type of professional. Show all of the pertinent steps as per the original instructions.

PART C Hypothesis Test of Proportions

1. According to data from the General Social Survey (GSS) on time use, the proportion of people aged 18 and over who went everywhere by car - as either a driver or a passenger - rose from 68% in 1992, to 70% in 1998 and then 74% in 2005. (From:https://www150.statcan.gc.ca)
2. An Albertan statistician believes that the proportion of people aged 18 and over who go everywhere by car has increased significantly from the value obtained by Statistics Canada in 2005. A random sample of 249 Albertans in the appropriate age group (ie. none under 18) were surveyed. 202 of those surveyed said that they go everywhere by car, rarely or never using public transit or other forms of travel.
3. Test the statistician's claim at a 10% level of significance. Show all of the 5 main steps of a proper hypothesis test (as demonstrated during in-class lessons).
4. Would your decision and conclusion change if you require a 1% level of significance? Show calculations to prove your point.
5. Would your decision and conclusion change if there were no prior study done by Statistics Canada (ie. you have no prior value of p to work with)?Show calculations to prove your point.