number 2 Statistics exam because they only useir work on Normal calculation quesnot considered clear communication. Tohnology in Step 2: normalcdflowermaking sure to carefully labople is the same as those weis new.and standard deviation for contis described by a density cfind the mean of the distribea under the density curvef solid material. The meany curves such as Normal c1 distribution from its infledeviation for most contindmined by the outcomeof a random variable gare two types of randossible values with gese values a probabilibilities is exactly 1.robabilities of all theaistogram, with theprobabilities on the-n interval on thedom variable isy curve directlyvent.am or densityive data-by..Use the mean to summarize the center of a probability distribution. Themean of a random variable x is the balance point of the probability distri-bution histogram or density curve.The mean is the long-run average value of the variable after many repeti-tions of the chance process. It is also known as the expected value of therandom variable, E(X).If X is a discrete random variable, the mean is the average of the values ofX, each weighted by its probability:Section 6.1 ExercisesMx = E(X)= Expx₁P1 + x₂P₂ + x3P3 + ....Use the standard deviation to summarize the variability of a probability dis-tribution. The standard deviation of a random variable ox measures howmuch the values of the variable typically vary from the mean.If X is a discrete random variable, the variance of X is the "average"squared deviation of the values of the variable from their mean:ok = Σ(x; -mx)²p; = (x₁ - MX) ²P₁ + (x₂ - Mx) ² P₂ + (x3 - MX) ²p3 + ...The standard deviation of X is the square root of the variance.Section 6.1Exercises1. Kids and toys In an experiment on the behavior ofpg 363 young children, each subject is placed in an area withfive toys. Past experiments have shown that the proba-bility distribution of the number X of toys played withby a randomly selected subject is as follows:6.1 Technology CornerTI-Nspire and other technology instructions are on the book's websiteat highschool.bfwpub.com/tps6e.12. Analyzing discrete random variablesPage 370Number of toys x₁ 01 23 4 5Probability p 0.03 0.16 0.30 0.23 0.17 ???375(a) Write the event "child plays with 5 toys" in terms of X.Then find its probability.(b) What's the probability that a randomly selected subjectplays with at most 3 toys?2. Spell-checking Spell-checking software catches "non-word errors," which result in a string of letters thatis not a word, as when "the" is typed as "teh." Whenundergraduates are asked to write a 250-word essay(without spell-checking), the number Y of nonworderrors in a randomly selected essay has the followingprobability distribution.аValue y0 1 2 3 4Probability p 0.1 ??? 0.3 0.3 0.1(a) Write the event "one nonword error" in terms of Y.Then find its probability.(b) What's the probability that a randomly selected essayhas at least two nonword errors?3. Get on the boat! A small ferry runs every half hourfrom one side of a large river to the other. The proba-bility distribution for the random variable Y = moneycollected (in dollars) on a randomly selected ferry tripis shown here.Money collectedProbability0 5 10 15 20 250.02 0.05 0.08 0.16 0.27 0.42(a) Find P(Y< 20). Interpret this result.(b) Express the event "at least $20 is collected" in termsof Y. What is the probability of this event?

For the variable, Y as the number of non-words errors, the incomplete probability distribution is…

1. Kids and toys In an experiment on the behavior of Pyoung children, each subject is placed in an area with five toys. Past experiments have shown that the proba- bility distribution of the number X of toys played with by a randomly selected subject is as follows: Number of toys x, Probability p 0 1 2 3 4 5 0.03 0.16 0.30 0.23 0.17 ??? (a) Write the event "child plays with 5 toys" in terms of X. Then find its probability. (b) What's the probability that a randomly selected subject plays with at most 3 toys? 2. Spell-checking Spell-checking software catches "non- word errors," which result in a string of letters that is not a word, as when "the" is typed as "teh." When undergraduates are asked to write a 250-word essay (without spell-checking), the number Y of nonword errors in a randomly selected essay has the following probability distribution. Value y Probability P 0 1 2 3 4 0.1 ??? 0.3 0.3 0.1 (a) Write the event "one nonword error" in terms of Y. Then find its probability. (b) What's the probability that a randomly selected essay has at least two nonword errors? 3. Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The proba- bility distribution for the random variable Y = money collected (in dollars) on a randomly selected ferry trip is shown here. Money collected Probability 5 10 15 20 25 0.02 0.05 0.08 0.16 0.27 0.42 (a) Find P(Y<20). Interpret this result. (b) Express the event "at least $20 is collected" in terms of Y. What is the probability of this event?

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P