Linear Transformation and Combination Pull Together Questions

A fleet of cars from Ford has an average MPG of 24 with a standard deviation of 4 mpg. Ford installs a new chip in the computers that will increase the gas mileage by 20%. What will the mean and standard deviation of the new MPG’s be?

• Mean: 28.8 MPG, Standard Deviation: 4.8 MPG

• Mean: 28.8 MPG, Standard Deviation: 4 MPG

• Mean: 24 MPG, Standard Deviation: 4.8 MPG

• Mean: 24 MPG, Standard Deviation: 4 MPG

Mr. Greider wants to curve his Calculus test scores. They currently have an average of 66 with a standard deviation of 5 points. His highest score was an 80, so he decided to double every score and then subtract 60 points. What would be the new expected mean and standard deviation? What problem might this cause for students that scored below a 60?

• The new expected mean is 72 and the standard deviation is 10. Students scoring below 60 will have negative scores.

• The new expected mean is 66 and the standard deviation is 5. Students scoring below 60 will have scores above 60.

• The new expected mean is 132 and the standard deviation is 10. Students scoring below 60 will have scores above 60.

• The new expected mean is 72 and the standard deviation is 5. Students scoring below 60 will have negative scores.

Mrs. Day decides to curve her Statistics scores. The mean of the scores was a 71 with a standard deviation of 3 points. She uses the curve: new score = 1.1(old score) + 10. What would be the new score of a student that scored a 76?

• 83.6

• 93.6

• 86.6

• 96.6

Jesse tracks his number of miles run for the past week and finds that he runs an average of 5.3 miles per day with a standard deviation of 1.1 miles. He makes it a goal to improve that by 1.5 miles per day. What would he expect his new mean and standard deviation of miles run per day to be?

• 6.8 miles mean, 1.1 miles standard deviation

• 5.3 miles mean, 2.6 miles standard deviation

• 6.8 miles mean, 2.6 miles standard deviation

• 7.0 miles mean, 1.1 miles standard deviation

A local bank charges a $20 service fee per month and pays out 2% interest. These transactions happen consecutively on the same day. Typically, the bank applies the interest first and then takes out the $20 service fee. The mean bank account balance before these successive transactions is $4,200 with a standard deviation of $125. What is the new mean balance after these transactions?

• $4,264

• $4,200

• $4,184

• $4,100

Mike, Steve and Phil are going to compete in a triathlon relay. Mike will do the swimming leg. He can typically do the swim in an average of 23 minutes with a standard deviation of 5 minutes. Steve will do the run. He typically does the run in an average of 55 minutes with a standard deviation of 6 minutes. Phil will do the bike. His average bike time is 46 minutes with a standard deviation of 3 minutes. What should they expect the mean and standard deviation of their combined times to be?

• Mean: 124 minutes, Standard Deviation: 14 minutes

• Mean: 124 minutes, Standard Deviation: 7.81 minutes

• Mean: 124 minutes, Standard Deviation: 8.37 minutes

• Mean: 124 minutes, Standard Deviation: 9.27 minutes

A company wants to sell trail mix. They decide to mix M&M’s with peanuts. Weights of bags of M&M’s have a mean of 7.6 ounces with a standard deviation of 1.3 ounces. Bags of peanuts that will be mixed with the M&M’s have a mean weight of 6.5 ounces with a standard deviation of 0.9 ounces. When the bags are mixed what is the expected combined mean and standard deviation?

• Mean: 14.1 ounces, Standard Deviation: 1.6 ounces

• Mean: 14.1 ounces, Standard Deviation: 2.2 ounces

• Mean: 14.1 ounces, Standard Deviation: 1.1 ounces

• Mean: 14.1 ounces, Standard Deviation: 2.0 ounces

Mr. White’s test scores for a very easy test are calculated and found to have an average of 87 with a standard deviation of 6 points. He then realizes he mistakenly added 10 points for an extra credit assignment to all the test scores instead of a homework assignment. When he takes those 10 points off (boo) what will the new mean and standard deviation of the test scores be?

• Mean: 77, Standard Deviation: 6

• Mean: 87, Standard Deviation: 6

• Mean: 77, Standard Deviation: 0

• Mean: 87, Standard Deviation: 0

The city’s radar detectors are malfunctioning. They have been over estimating the speeds of cars by 3 mph. (Measured speeds = Actual speeds + 3). If the city has been measuring cars speed and found the mean to be 72 mph with a standard deviation of 4 mph, what can they expect the new values to be after the speeds are adjusted?

• Mean: 69 mph, Standard Deviation: 4 mph

• Mean: 72 mph, Standard Deviation: 4 mph

• Mean: 75 mph, Standard Deviation: 4 mph

• Mean: 69 mph, Standard Deviation: 7 mph

The number of grains of coffee found in a brewed espresso has a mean of 12 grains with a standard deviation of 2 grains. Quality control is trying out new filters that claim to reduce the number of grains allowed through by half. They also claim that using filtered water can decrease the number of grains that make it through the filter by three on average. The equation for this transformation is $ y = 0.5x - 3 $. What is the mean and standard deviation for the number of grains in the drink if both new measures are used?

• Mean: 3 grains, Standard Deviation: 1 grain

• Mean: 6 grains, Standard Deviation: 1 grain

• Mean: 3 grains, Standard Deviation: 2 grains

• Mean: 6 grains, Standard Deviation: 2 grains