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

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°