A coin is weighted so that the probability of obtaining a head in a single toss is 0.3. If the coin is tossed 35 times, what is the probability of obtaining between 9 and 14 heads, exclusive. a. 0.510 b. 0.627 c. 0.701 d. 0.287 e. 0.824 9. If 14% of men are bald, what is the probability that more than 100 in a random sample of 850 men are bald?a. 0.9778
b. 0.9664
c. 0.0697
d. 0.0027
e. 0.0378The Colorado Mining and Mineral Company has 1000 employees engaged in its mining operations. It has been estimated that the probability of a worker meeting with an accident during a 1-yr period is 0.08. What is the probability that more than 70 workers will meet with an accident during the 1-yr period?
a. 0.8665
b. 0.9089
c. 0.3585
d. 0.3827
e. 0.5753

(1) The correct answer is option (a) 0.510

(2) The correct answer is option (b) = 0.9664

(3) The correct answer is option (a)  0.8665

Step-by-step explanation:

1. Find attached of question 1

2.

n=850

p=0.1400  

here mean of distribution(μ) =n*p

                                               =850* 0.1400

                                                = 119  

standard deviation σ = √(np(1-p))

                                    = √(850*0.1400(1-0.1400))

                                    = √102.34

                                       =10.1163  

for normal distribution z score =(X-μ)/σx    

therefore from normal approximation of binomial distribution and continuity correction:

probability =P(X>100.5)

                   =P(Z>-1.83)

                   =1-P(Z<-1.83)

                   =1-0.0336

                   =0.9664

3.

n = 1000

p = 0.08

mean of distribution(μ) =np

                                       = 1000*0.08

                                        = 80

and standard deviation σ=√(np(1-p))

                                    = √(1000*0.08(1-0.08))

                                    = √736

                                    = 8.5790

probability =P(X>70.5)

                   =P(Z>-1.11)

                    =1-P(Z<-1.11)

                    =1-0.1335

                    =0.8665

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

a=r

d=q

c=p

b=s

hope this !