Homework #4--Suggested Answers

1) ISBE 3.25, 3.26, 3.27

2) ISBE 4.1, 4.4, 4.7, 4.8

3) ISBE 4.11, 4.12, 4.13.(b)

 

3.25) Pr(cancer | + reaction) = ((0.003*0.98)/(0.003*0.98 + 0.997*0.05)) = 0.056

3.26) Pr(rain | barometer says rain) = ((0.4 * 0.9)/(0.4*0.9 + 0.6*0.3)) = 0.667

3.27)

  1. Pr(poor shipment) = 300/(300+900) = 1/4 = 0.25
  2. Pr(poor shipment | draw defective saw) = ((0.25*0.4)/(0.25*0.4 + 0.75*0.1)) = 0.57

 

4.1) Assuming that boys and girls are equally likely:

a. distribution of number of girls

X

p(x)

0

1*(1/8)=0.125

1

3*(1/8)=0.375

2

3*(1/8)=0.375

3

1*(1/8)=0.125

 

b. distribution of number of runs

y

p(y)

1

0.25

2

0.50

3

0.25

 

 

4.4

a.

x

p(x)

0

0.008

1

0.096

2

0.384

3

0.512

 

 

    0.384 + 0.512 = 0.896, or 89.6%

 

4.7)

  1. Mean = 62, Standard Deviation = 9.5
  2. 80%, 20%
  3. 70

 

4.8)

  1. Mean attendance = 33,000
  2. At $9 a ticket the expected total revenue would be $297,000. After costs ($276,000) the producer would expect to net $21,000--but there is a 50% chance that he will lose money or break even.

 

4.11)

0.442 (could use table III(c), pp 772-773.).

 

4.12)

  1. n=100, p =0.5, mean = 50
  2. n=30, p =1/6, mean = 5
  3. n=20, p =0.5, mean = 10
  4. mean = n*p

 

4.13)

b. m =2.4, s =1.39