The manufacturer of the colorsmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. in order to test this claim, a consumer group randomly selects 420 consumers who have owned a colorsmart-5000 television set for five years. of these 420 consumers, 303 say their colorsmart-5000 television sets did not need a repair, whereas 117 say their colorsmart-5000 television sets did need at least one repair. (a) find a 99 percent confidence interval for the proportion of all colorsmart-5000 television sets that have lasted at least five years without needing a single repair.

(0.665 , 0.777)

Step-by-step explanation:

Given : Sample size of consumers: n=420  ;

Number of consumers say their ColorSmart-5000 television sets did not need a repair=303

The the sample proportion for consumers say their ColorSmart-5000 television sets did not need a repair :

Significance level :

Critical value =

The confidence interval for population proportion is given by :_

i.e.  

Hence,  a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years without needing a single repair = (0.665 , 0.777)

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

2.56 is the width of the garden

step-by-step explanation: