A survey classified a large number of adults according to whether they were judg

Question

A survey classified a large number of adults according to whether they were judged to need eyeglasses to correct their reading vision and whether they used eyeglasses when reading. The proportions falling into the four categories are shown in the table. (Note that a small proportion, 0.03, of adults used eyeglasses when in fact they were judged not to need them.)

If a single adult is selected from this large group, find the probability of each event. (Enter your answers to two decimal places.)

(a) The adult is judged to need eyeglasses.


(b) The adult needs eyeglasses for reading but does not use them

(c) The adult uses eyeglasses for reading whether he or she needs them or not.

In a genetics experiment, the researcher mated two Drosophila fruit flies and observed the traits of 300 offspring. The results are shown in the table.

One of these offspring is randomly selected and observed for the two genetic traits.

(a) What is the probability that the fly has normal eye color and normal wing size? (Enter an exact number as an integer, fraction, or decimal.)


(b) What is the probability that the fly has vermillion eyes? (Enter an exact number as an integer, fraction, or decimal.)


(c) What is the probability that the fly has either vermillion eyes or miniature wings, or both? (Enter an exact number as an integer, fraction, or decimal.)

Suppose that

P(A) = 0.3

and

P(B) = 0.2.

If events A and B are independent, find these probabilities. (Enter your answers to two decimal places.)(a)    

P(A B)

(b) P(A B)

The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life of the drug—that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here.

(a) Find the expected number of years of patent life for a new drug. (Enter your answer to two decimal places.)


(b) Find the standard deviation of x. (Round your answer to four decimal places.)

(c) Find the probability that x falls into the interval ± 2. (Enter your answer to two decimal places.

Used Eyeglasses
for Reading Judged to Need
Eyeglasses Yes No Yes 0.44 0.15 No 0.03 0.38

Explanation / Answer

(a) The adult is judged to need eyeglasses.

=0.44+0.15=0.59
(b) The adult needs eyeglasses for reading but does not use them=0.15

(c) The adult uses eyeglasses for reading whether he or she needs them or not.=0.44+0.03=0.47

(a) What is the probability that the fly has normal eye color and normal wing size? (Enter an exact number as an integer, fraction, or decimal.)
=135/300=0.45

(b) What is the probability that the fly has vermillion eyes? (Enter an exact number as an integer, fraction, or decimal.)=157/300=0.52


(c) What is the probability that the fly has either vermillion eyes or miniature wings, or both? (Enter an exact number as an integer, fraction, or decimal.)

=(157+162-154)/300=0.55

(a) P(A B)=P(A)*P(B)=0.3*0.2=0.06

(b) P(A B)=P(A)+P(B)-P(A B)=0.3+0.2-0.06=0.44

mean=E(x)=sum(x*p(x))= 7.9

E(x2)=sum(x2*p(x))=67.14

var(x)=E(x2)-E(x)2=67.14-7.9*7.9=

sd(x)=sqrt(4.73)=2.17

P( ± 2)=0.9544

x 3 4 5 6 7 8 9 10 11 12 13 sum p(x) 0.03 0.05 0.07 0.1 0.14 0.2 0.18 0.12 0.07 0.03 0.01 1 x*p(x) 0.09 0.2 0.35 0.6 0.98 1.6 1.62 1.2 0.77 0.36 0.13 7.9 x2*p(x) 0.27 0.8 1.75 3.6 6.86 12.8 14.58 12 8.47 4.32 1.69 67.14

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