DISTRIBUTIONSstretches toward the higher values of x. The mean of the distribution n = 8 and p = .80 is6.4, which results in the highest probabilities being near x = 6 and x = 7. Thus the peak ofthe distribution is nearer to 8 than to 0 and the distribution stretches back toward x = 0.In any binomial distribution the largest x value that can occur is n and the smallestvalue is zero. Thus the graph of any binomial distribution is constrained by zero and n. Ifthe p value of the distribution is not .50, this constraint will result in the graph "piling up"at one end and being skewed at the other end.A manufacturing company produces 10,000 plastic mugs per week. This companysupplies mugs to another company, which packages the mugs as part of picnic sets.The second company randomly samples 10 mugs sent from the supplier. If two orfewer of the sampled mugs are defective, the second company accepts the lot. Whatis the probability that the lot will be accepted if the mug manufacturing companyactually is producing mugs that are 10% defective? 20% defective? 30% defective?40% defective?SolutionIn this series of binomial problems, n = 10, x ≤ 2, and p ranges from .10 to .40. FromTable A.2-and cumulating the values-we have the following probability of x ≤ 2 foreach p value and the expected value (= n. p).Expected NumberLot AcceptedPix ≤ 2)of Defects (μ)Р.10.9301.0.20.6772.0.30.3823.0.40.1674.0These values indicate that if the manufacturing company is producing 10%defective mugs, the probability is relatively high (.930) that the lot will be acceptedby chance. For higher values of p, the probability of lot acceptance by chancedecreases. In addition, as p increases, the expected value moves away from theacceptable values, x≤ 2. This move reduces the chances of lot acceptance.5.5Solve the following problems by using the binomial formula.a.If n = 4 and p = .10, find P(x = 3).b. If n = 7 and p = .80, find P(x = 4).C.If n = 10 and p = .60, find P(x ≥ 7).d. If n = 12 and p = .45, find P(5 ≤ x ≤ 7).Solve the following problems by using the binomial tables (Table A.2).a.If n = 20 and p = .50, find P(x = 12).b. If n = 20 and p = .30, find P(x 8).C.If n = 20 and p = .70, find P(x

Question

DISTRIBUTIONSstretches toward the higher values of x. The mean of the distribution n = 8 and p = .80 is6.4, which results in the highest probabilities being near x = 6 and x = 7. Thus the peak ofthe distribution is nearer to 8 than to 0 and the distribution stretches back toward x = 0.In any binomial distribution the largest x value that can occur is n and the smallestvalue is zero. Thus the graph of any binomial distribution is constrained by zero and n. Ifthe p value of the distribution is not .50, this constraint will result in the graph &#34;piling up&#34;at one end and being skewed at the other end.A manufacturing company produces 10,000 plastic mugs per week. This companysupplies mugs to another company, which packages the mugs as part of picnic sets.The second company randomly samples 10 mugs sent from the supplier. If two orfewer of the sampled mugs are defective, the second company accepts the lot. Whatis the probability that the lot will be accepted if the mug manufacturing companyactually is producing mugs that are 10% defective? 20% defective? 30% defective?40% defective?SolutionIn this series of binomial problems, n = 10, x ≤ 2, and p ranges from .10 to .40. FromTable A.2-and cumulating the values-we have the following probability of x ≤ 2 foreach p value and the expected value (= n. p).Expected NumberLot AcceptedPix ≤ 2)of Defects (μ)Р.10.9301.0.20.6772.0.30.3823.0.40.1674.0These values indicate that if the manufacturing company is producing 10%defective mugs, the probability is relatively high (.930) that the lot will be acceptedby chance. For higher values of p, the probability of lot acceptance by chancedecreases. In addition, as p increases, the expected value moves away from theacceptable values, x≤ 2. This move reduces the chances of lot acceptance.5.5Solve the following problems by using the binomial formula.a.If n = 4 and p = .10, find P(x = 3).b. If n = 7 and p = .80, find P(x = 4).C.If n = 10 and p = .60, find P(x ≥ 7).d. If n = 12 and p = .45, find P(5 ≤ x ≤ 7).Solve the following problems by using the binomial tables (Table A.2).a.If n = 20 and p = .50, find P(x = 12).b. If n = 20 and p = .30, find P(x > 8).C.If n = 20 and p = .70, find P(x < 12).d. If n = 20 and p = 90, find5.6

Accepted Answer

“Since you have asked multiple question, we will solve the first question and three sub-parts for…

5.5 Solve the following problems by using the binomial formula. If n = 4 and p = .10, find P(x = 3). If n = 7 and p = .80, find P(x = 4). If n = 10 and p = .60, find P(x ≥ 7). If n = 12 and p = 45, find D a. b. c. d.