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Mama L [17]
2 years ago
13

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

Mathematics
1 answer:
Vlada [557]2 years ago
8 0

Answer:

(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

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-2<em>x</em> + 6<em>y</em> = -38

3<em>x</em> - 4<em>y</em> = 32

To solve by elimination, multiply the top equation by 3 and the bottom equation by 2.

3(-2<em>x</em> + 6<em>y</em> = -38) --> -6<em>x</em> + 18<em>y</em> = -114

2(3<em>x</em> - 4<em>y</em> = 32) --> 6<em>x</em> - 8<em>y</em> = 64

Add the equations.

-6<em>x </em>+ 18<em>y</em> = -114

6<em>x</em> - 8<em>y</em> = 64

+_____________

0 + 10<em>y</em> = -50

10<em>y</em> = -50

<em>y</em> = -5

Substitute -5 for y into one of the original equations to find x.

3<em>x</em> - 4<em>y</em> = 32

3<em>x</em> - 4(-5) = 32

3<em>x</em> + 20 = 32

3<em>x</em> = 12

<em>x</em> = 4

Check work by plugging the <em>x</em>- and <em>y</em>-values into both of the original equations.

-2<em>x</em> + 6<em>y</em> = -38

-2(4) + 6(-5) = -38

-8 - 30 = 38

38 = 38


3<em>x</em> - 4<em>y</em> = 32

3(4) - 4(-5) = 32

12 + 20 = 32

32 = 32

Answer:

<em>x</em> = 4 and <em>y</em> = -5; (4, -5).

8 0
3 years ago
Read 2 more answers
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