1. Let 'x' be the number of emergency root canal surgeries performed by Dr. Sharps on a given Monday. The following table lists the proba10.282.3.5.XP(x)6.a.b.C.00.13C.d.20.30Sketch a frequency histogram for the given PDF above.Calculate the mean, variance and standard deviation for the given PDF.Give a brief representation of the value of the mean.At the Bank of America, past data show that 8% of all credit card holders' default at some time in their lives. On a recent day, this bank issued twelve creditIcards to new customers. Find the probability that of these twelve customers, eventually:a.exactly three will default on their credit cards.b.at least six will default on their credit cards.a.b.C.4. There is an average of 6.3 robberies occur per day in a large city.30.17at most four will default on their credit cards.Calculate the mean, variance and standard deviation of this distributionthatGeneral Electric buys certain parts for its refrigerators from Best Buy Corporation. The parts are received in shipments of 400 boxes, each containing sixteenbox. The qualitybox. The shipment is accepted if at most one of the four parts is defect selecte quellty control inspector at General Electric selected a box from a recentlyreceived shipment of such parts. This is unknown to the inspector when the box contains three defective parts.a.What is the probability that this shipment will be accepted?b.What is the probability that this shipment will not be accepted?Find the mean, variance and standard deviation of the distribution.C.40.0850.04Find the probability that on a given day that exactly three robberies will occur in this city.Calculate the mean, variance and standard deviation.Find the probability that on a given day that the number of robberies that will occur in this city isexactly sixat most threebetween the values of two and fiveSix Flags Great Adventure amusement park basketball games, the players get six throws for two dollars. If the player makes the basket, the player wins aprize. Mary makes sixty-two percent of her shots. Find the probability that Mary wins a prize on her fifth shot. Find the mean and standard deviation.The probability that a television contains zero, one, or two defects is 0.88, 0.08, and 0.04, respectively. In a sample of 16 televisions, find the probabilitythat 9 will have no defects, 4 will have one defect, and 3 will have two defects. Find the mean, variance and standard deviation.

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved, then please specify the question number or post only that question.The probability distribution of the number of emergency root canal surgeries performed by Dr. Shape is given as follows:x012345p(x)0.130.280.30.170.080.04Part (a)Considering the value of x (i.e., the number of emergency root canal surgeries performed) on the x-axis and the corresponding probability value, p(x) on the y-axis, the histogram for the given PDf is obtained as follows:Part (b)Calculation table:x012345Totalp(x)0.130.280.30.170.080.041x p(x)00.280.60.510.320.21.91x201491625x2 p(x)00.281.21.531.2815.29For the given discrete probability distribution, the mean is calculated as follows:E(x)=∑xp(x) [provided that ∑ip(xi)=1]=1.91The variance of the given discrete probability distribution is calculated as follows:V(x)=E(x2)−[E(x)]2=∑x2p(x)−[E(x)]2=5.29−1.912=1.6419The standard deviation of the given discrete probability distribution is calculated as follows:SD(x)=V(x)=1.6419=1.281366458Part (c)Here the value of the mean essentially represents the number of emergency root canal surgeries performed. In the given context, on average Dr. Shape is considered to have performed 1.91 emergency root canal surgeries on a given Monday.This average or the expected number of emergency root canal surgeries performed on a given Monday is the weighted average of the values of the number of surgeries performed on a given Monday with respective probabilities (or wrightage).(a) The histogram for the given PDf is:(b) For the given discrete probability distribution, the mean, variance, and standard deviation are calculated as 1.91, 1.6419, and 1.281366458 respectively.(c) In the given context, on average Dr. Shape is considered to have performed 1.91 emergency root canal surgeries on a given Monday.