Question

5) True or False: The diameters of 10 randomly selected bolts have a binomial distribution.              

A) True                 B) False

6) True or False: Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.      

A) True                 B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

7) If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .              

8) If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________.

9) If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________.

10) Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?     1

A) 65 days           B) 45 days            C) 81 days           D) 5 days

Answer 1

Note : Allowed to solve only 4 questions per post.

5) True or False: The diameters of 10 randomly selected bolts have a binomial distribution.
B) False

Explanation: For a binomial distribution, we need the outcome to binary, that true or false / yes or no. But in this case it continuous random variable and hence it cannot be considered as binomial distribution.

6) True or False: Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

A) True   

Explanation

We need to find the

P(X<2) = P(X= 0) + P(X=1)

We are given the following p = 0.1 9 = 1- p = 0.9 n = 10 x = 0 We need to find P(X=0). This is a binomial distribution and the formula is given below P(x) = (2-3):27 po* q** P(X = 0) = - 0.1° x 0.9(10-0) = 0.3486784 (10-0)!x0! 0. P(X = 0) =0.3486784

P(X = 1) = 0.10 0.11 x 0.9(10-1) = 0.3874205 P(X = 1)=0.3874205

P(X<2) =P(X= 0) + P(X=1)=0.3874+0.3486= 0.736

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

7) If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = 0.4116

We are given the following p = 0.3 q = 1-p = 0.7 n = 4 x = 1 We need to find P(X=1). This is a binomial distribution and the formula is given below P(x) = (27 yet powq"-* P(X=1 4 0 .31 x 0.7(4-1) = 0.4116 (4-1)!x1! U P(X = 1) =0.4116

8) If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = 0.3483.

P(X>1) = 1- P(X<=1)
But
P(X<=1) = P(X=0)+P(X=1)
Therefore we have
P(X>1) = 1- (P(X=0)+P(X=1))

P(X>1) = 1- (0.2401+0.4116)= 0.3483

We are given the following p = 0.3 q = 1- p = 0.7 n = 4 x = 0 We need to find P(X=0). This is a binomial distribution and the formula is given below P(x ) = (n-pt poq*** P(X = 0) = 0 .30 x 0.7(4-0) = 0.2401 !! 4 (4-0)! P(X = 0) =0.2401

9) If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = 0.0729

We are given the following p = 0.1 q = 1-p = 0.9 n = 5 X = 2 We need to find P(X=2). This is a binomial distribution and the formula is given below P(x) = (na let po q*-* P(X = 2) = - 5! 0.12 x 0.9(5-2) = 0.0729 (5-2)!x 2! P(X = 2)=0.0729