Introduction to Probability and Statistics for Engineers and Scientists

Problems 427

35.The proportion of a given heat rise that has dissipated a timetafter the source is

cut off is of the form

P= 1 −e−αt

for some unknown constantα. Given the data

P .07 .21 .32 .38 .40 .45 .51

t .1 .2 .3 .4 .5 .6 .7

estimate the value ofα. Estimate the value oftat which half of the heat rise is

dissipated.

36.The following data represent the bacterial count of five individuals at different

times after being inoculated by a vaccine consisting of the bacteria.

Days Since Inoculation Bacterial Count

3 121,000

6 134,000

7 147,000

8 210,000

9 330,000

(a) Fit a curve.

(b) Estimate the bacteria count of a new patient after 8 days.

37.The following data yield the amount of hydrogen present (in parts per million)

in core drillings of fixed size at the following distances (in feet) from the base of

a vacuum-cast ingot.

Distance 1 2 3 45678910

Amount 1.28 1.50 1.12 .94 .82 .75 .60 .72 .95 1.20

(a) Draw a scatter diagram.

(b) Fit a curve of the form

Y=α+βx+γx^2 +e

to the data.

38.A new drug was tested on mice to determine its effectiveness in reducing cancerous

tumors. Tests were run on 10 mice, each having a tumor of size 4 grams, by

varying the amount of the drug used and then determining the resulting reduction