MAT 152Section 3.1 and 3.2MCGINNISName:______________________________

1.Use the five test scores of 65, 70, 71, 75, and 95 to answer the following questions:

a)Find the sample mean - round to one decimal place.

b)Find the median.

c)Suppose the professor decides to curve the exam by adding 4 points to each test score.Compute the sample mean based on the adjusted scores.

d)Compare the unadjusted test score mean with the curved test score mean.What effect did adding 4 to each score have on the mean?

2.Determine which measure of central tendency ( MEAN, MEDIAN, or MODE) is most appropriate and justify your answer:The first one is answered for you.

a)Average price of a home sold in Hickory, NC in 2017?

Answer:The median should be used as the measure of center because we would expect the distribution of home prices to be skewed right (a few extremely high million dollar homes would skew the distribution)

b)Most popular major for students enrolled in a statistics course:

c)Average test score when the scores are distributed symmetrically?

d)Average test score when the scores are skewed right?

e)Average income of a player in the National Football League?

f)Most requested song at the radio station?

g)Typical number on the jersey of a player in the National Hockey League?

3.What does it mean for a statistic to be resistant?

Standard Deviation

4.The following data sets give samples of gas mileage (in miles per gallon) for two different cars.

Car ACar B

22.226.9

20.918.2

23.716.9

20.123.5

24.125.5

a)Find the mean for car A: _____________

b)Find the mean for car B: _____________

c)Find the range for car A: _____________

d)Find the range for car B: _____________

e)Find the standard deviation for car B: ______________

Use StatCrunch or the formula:

f)The standard deviation for car A is approximately 1.73.Based on the gas mileage, which car would you buy?Explain your choice using appropriate vocabulary regarding measures of central tendency and dispersion.

6.A certain brand of lightbulbs has a mean life of 600 hours and a standard deviation of 53 hours.The life of lightbulbs is normally distributed. (Suggestion:first draw a normal curve and label 1, 2, and 3 standard deviations on both sides)

a)According to the Empirical Rule, 68% of lightbulbs have lifetimes between __________________

and _________________ hours.

b)What percent of lightbulbs will last between 600 and 759 hours?_________________

c)If a lightbulb burns out before 441 hours, the customer is eligible for a 150% money-back refund.

What percent of lightbulbs will warrant the refund?_________________