QUESTION # 1

Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Letxbe a random variable representing time to failure (in hours) at 90% breaking strength.

0.55 1.80 1.52 2.05 1.031.180.801.331.291.13

3.341.540.080.120.600.720.921.051.433.03

1.812.170.630.560.030.090.180.341.511.45

1.520.191.550.020.070.650.400.241.511.45

1.601.804.690.087.891.581.640.030.230.72

(a) Find the range.

(b) Use a calculator to calculatexandx². (Round your answers to two decimal places.)x=x²=

(c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to two decimal places.)x=s²=s=

(d) Use the results of part (c) to compute the coefficient of variation. (Round your answer to the nearest whole number.)

%

QUESTION # 2

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set9,4,13,11,9.

(a) Use the defining formula, the computation formula, or a calculator to computes. (Round your answer to one decimal place.)

s=

(b) Multiply each data value by8to obtain the new data set72,32,104,88,72. Computes. (Round your answer to one decimal place.)

s=

(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constantc?

Multiplying each data value by the same constantcresults in the standard deviation increasing bycunits.

Multiplying each data value by the same constantcresults in the standard deviation remaining the same.

Multiplying each data value by the same constantcresults in the standard deviation being |c| times smaller.

Multiplying each data value by the same constantcresults in the standard deviation being |c| times as large.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to bes=2.5miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

Yes

No

Given 1 mile1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)

s=km

QUESTION # 3

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

5,9,8,8,17

(a) Use the defining formula, the computation formula, or a calculator to computes. (Enter your answer to one decimal place.)

(b) Add7to each data value to get the new data set12,16,15,15,24. Computes. (Enter your answer to one decimal place.)