Question

1. An instructor grades exams, 20%; term

paper, 30%; final exam, 50%. A student had grades of

83, 72, and 90, respectively, for exams, term paper, and

final exam. Find the student’s final average. Use the

weighted mean.

2. Stories in the Tallest Buildings The number of

stories in the 13 tallest buildings for two different

cities is listed below. Which set of data is more

variable?

Houston: 75, 71, 64, 56, 53, 55, 47, 55, 52, 50, 50, 50, 47

Pittsburgh: 64, 54, 40, 32, 46, 44, 42, 41, 40, 40, 34, 32, 30

3. Americans spend an average of

3 hours per day online. If the standard deviation is

32 minutes, find the range in which at least 88.89%

of the data will lie. Use Chebyshev’s theorem.

4. The average farm in the United States in

2004 contained 443 acres. The standard deviation is

42 acres. Use Chebyshev’s theorem to find the

minimum percentage of data values that will fall in

the range of 338–548 acres.

5. The average age of senators in

the 108th Congress was 59.5 years. If the standard

deviation was 11.5 years, find the z scores

corresponding to the oldest and youngest senators:

Robert C. Byrd (D, WV), 86, and John Sununu

(R, NH), 40.

      7. Which score indicates the highest relative position?

a. A score of 3.2 on a test with mean 4.6 and

s 1.5

b. A score of 630 on a test with mean 800 and

s 200

c. A score of 43 on a test with _mean 50 and s 5

Answer 1

(1)

Value (x)	Weight (w)	x w
83	0.20	16.6
72	0.30	21.6
90	0.50	45.0
Total=	1.00	83.2

Weighted mean= 83.1/1 = 83.1

So,

Answer is:

83.1

(2)

From the given data, the following statistics are calculated:

Houston:

n = 13

= 55.7692

s = 8.8803

Pittsburgh :

n = 13

= 41.4615

s = 9.4217

Since the standard deviation of Pittsburgh= 9.4217 is greater than the standard deviation of Houston = 8.8803, Pittsburgh set of data is more variable.

(3)

= 3 X 60 = 180

= 32

By Chebyshev's Theorem:

So,

So,

k = 3.0

So,

Range is:

180 - (3 X 32) to 180 + (3 X 32)

i.e.,

180 - 96 to 180 +96

i.e.,

84 to 276

(4)

= 443

= 42

X =338

k = (338 - 443)/42

= - 2.5

By Chebyshev's Theorem:

                =84%

So

Answer is:

84%

(5)

Robert C. Bryd:

= 59.5

= 11.5

X = 86

Z = (86 - 59.5)/11.5 = 2.3043

John Sununu:

= 59.5

= 11.5

X = 40

Z = (40 - 59.5)/11.5 = - 1.6957

So,

Answers are:

2.3043 and - 1.6957

(7)

(a)

= 4.6

= 1.5

X = 3.2

Z = (3.2 - 4.6)/1.5 = - 0.9333

(b)

= 800

= 200

X = 630

Z = (630 -800)/200 = - 0.85

(c)

= 50

= 5

X = 43

Z = (43 - 50)/5 = - 1.40

Score (b) indicates the highest relative position since z score of (b) = - 0.85 is the highest z score.