MATHEMATICS

Exam Review

 

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot, and summary statistics are shown below.

  1. Comment on whether each of the following conditions for correlation / linear regression is met.
    1. Quantitative variable condition.
    2. Linearity condition.
    3. Outlier condition.

  2. Estimate the linear regression model that relates the response variable (monthly sales) to the predictor variable (price per pound).
    1. Find the slope of the regression line.
    2. Find the intercept of the regression line.
    3. Write the equation of the linear model.
  1. Using the estimated regression equation,
    1. Estimate the monthly sales for a variety of coffee that costs $12 per pound.
    2. What is the residual for this estimate? What does it mean?

  2. During a promotion, Christina’s department store offers a mailing “scratch a winnerdiscount savings.” After customers select the items they wish to purchase, they scratch their discount sticker from the mailing to determine the discount they will receive. The scratch wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount if the customer scratches that slice!

    1. What is the probability that a customer gets at least a 40% discount?
    2. What is the probability that a customer does not get at least a 40% discount?
    3. What is the probability that a customer gets a 10% or 20% discount?
    4. What is the probability that two customers in a row get a 20% discount?

6) A recent survey of local cell phone retailers showed that of all smart phones sold last month, 64% of buyers also owned a tablet of laptop, 28% also owned an iPod type music player and 22% owned both.

  1. What is the probability that a smart phone buyer also owned a tablet/ laptop or a musicplayer?
  2. What is the probability that a smart phone buyer did not also own either a tablet/ laptopor a music player?
  3. Is a smart phone buyer owning a tablet/laptop in addition to a music player mutuallyexclusive? Explain.
6)

  1. One explanation put forth for the dearth of women CEO’s in the high tech industry is that 7) there are a lack of mentoring opportunities for women. A recent survey of CEO’s in that industry found that 80% were men. Moreover, 75% had been mentored while only 15% were women and had been mentored.
    1. Construct the contingency table.
    2. Are gender and mentoring independent? Explain.

  2. A fast food restaurant just leased a new freezer and food fryer for three years. The service 8) contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant’s research indicates that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.
    1. Find the expected number of repairs for this freezer per year.
    2. Find the standard deviation of the number of repairs per year.
    3. What are the mean and standard deviation of the restaurant’s annual expense with theservice contract for the freezer?

  3. Internet service providers (ISP) need to resolve customer problems as quickly as possible.

For one ISP, past data indicates that the likelihood is 0.80 that customer calls regarding Internet service interruptions are resolved within one hour. Out of the next 10 customer calls about interrupted service,

      1. What is the probability that exactly 7 will be resolved within one hour?
      2. What is the probability that at least 7 will be resolved within one hour?
      3. How many customers would be expected to have their service problems resolved withinone hour?

  1. At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes.
    1. What percent of new machine set ups take more than 30 minutes?
    2. The typical worker needs five minutes to adjust to their surroundings before beginningtheir duties. What percent of new machine set ups are completed within 25 minutes to allow for this?
      11) Porcelain tile is often recommended over ceramic tile because its breaking strength tends to be higher therefore making it more durable and long lasting. Based on data collected from its production processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch.

      1. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths between 375 and 425 pounds per square inch?
      2. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch?
      3. Based on the 68-95-99.7 Rule, describe the breaking strength of the weakest 2.5% of its popular porcelain tile.
      11)

      1. A specific automotive part that a service station stocks in its inventory has an 8% chance of being defective. Suppose many cars come into the service station needing this part each week.
        1. What is the probability that the fourth part retrieved from stock is the first defective?
        2. What is the probability that the tenth part retrieved from stock is defective?
        3. What is the expected number of parts retrieved until the first defective part?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

      1. The option to buy extended warranties is commonplace with most electronics purchases. But doesthe type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.

 

  Purchased Warranty?  
  Yes No Total
Digital Camera 30 42 72
Laptop Computer 145 203 348
Total 175 245 420

 

 

 

 

 

 

 

 

The probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera is

A) .83 B) .42 C) .07 D) .17 E) .58

14) As accounts manager in your company, you classify 75% of your customers as “good credit” and the rest as “risky credit” depending on their credit rating. Customers in the “risky” category allow their accounts to go overdue 50% of the time on average, whereas those in the “good” category allow their accounts to become overdue only 10% of the time. What percentage of overdue accounts are held by customers in the “risky credit” category?

A) 12.5% B) 62.5% C) 20% D) 93.75%

 

15) It is estimated that 20% of luxury cars manufactured in 2012 were silver. A car dealership typically sells 20 luxury cars per month. The probability that 8 of the luxury cars sold per month are silver is

 

A) 0.0222.

B) 0.0006.

    1. None of these.
    2. 0.7779.
    3. 0.1276.

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