For X ∼Bin(100, 1/3 ), set up, but do not calculate, expressions that approximatethe following probabilities. The expressions must be of the form P (z1 ≤ Z ≤ z2) whereZ ∼ N (0, 1):(a) P (30 ≤ X ≤ 35)(b) P (90 ≤ X ≤ 100)

For X ∼Bin(100, 1/3 ), set up, but do not calculate, expressions that approximatethe following probabilities. The expressions must be of the form P (z1 ≤ Z ≤ z2) whereZ ∼ N (0, 1):(a) P (30 ≤ X ≤ 35)(b) P (90 ≤ X ≤ 100)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: A random variable X is distributed as N (69, 9). Find the probability that the value of a randomly…

A: We have given information, A random variable X is distributed as N69, 9 i.e. μ=69 σ2=9 ⇒σ=3

Q: Let X - Geom(p). Let s 2 0 be an integer. Show that P(X > s) = (1 – p)s. (Hint: The probability that…

A: Geometric distribution In series of Bernoulli trials, the random variable X denotes number of trials…

Q: (a) the probability of transmitting (1) with condition of receiving (1) at the receiver end. (b) the…

A: Given, P(m1) = 0.45 So, P(m0) = 1-0.45 = 0.55 P(B0|m0) = 0.40, So, P(B1|m0) = 1-0.4 =0.60 P(B0|m1)…

Q: A container contains 35 green tokens, 20 blue tokens, and 3 red tokens. Two tokens are randomly…

A: From the given information, there are 35 green tokens, 20 blue tokens and 3 red tokens. Total number…

Q: In a game played with dice, Ali or Bob is selected with a probability of 5 and , respectively. The…

A: Given that in a game played with throwing a four sided dice twice, Ali or Bob is selected with a…

Q: A fair coin is tossed three times. Let R, S and T be three events such tha R: maximum one coin shows…

A: It is given that a fair coin is tossed three times. Therefore, Sample space is:…

Q: a student takes a true false test that has 6 questions and guests randomly at each answer. Let x be…

Q: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will throw the same die…

A: Given information: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will…

Q: It is claimed that 60% of all students at a college still need to take another math class. Baseed on…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted.Sample…

Q: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will throw the same die…

A: Given information: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will…

Q: We will define the conditional probability of A given X as any random vari- able P(AIX) over (N, F,…

A: To prove that two versions of differ in a set of probability zero, we'll use a proof by…

Q: Each of 12 laptops was returned to the dealer due to a strange sound from the fan when they were…

A: The number of laptops are 12. The number of faulty laptops are 7. The number of laptops have less…

Q: 8. Suppose Pr(E | H) > Pr(E). When is Pr(H | E) > 1/2 then? Assume all conditional probabilities are…

A: We know that the formula of conditional probability isWe use this concept to find the answer to…

Q: A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain…

A: Introduction - Probability distribution of binomial distribution is given by Px=nxpxqn-xwhere , P…

Q: Identify the stronger prior from each of the pairs below: (a) Beta(5, 10), Beta(7, 7). (b) N(5,8), N…

A: The mean of a Beta distribution with parameters (α, β) is given by the formula: Mean=α(α + β)

Q: We can use inclusion-exclusion with conditional probabilities of the form P(A∪B∣C). Can we also do…

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: 2. Assume that the prices paid for housing within a neighborhood have a normal distribution, with…

A: We have given information, Assume that X be the prices paid for housing within a neighborhood have a…

Q: + ∞P₂(A) is also a probability. 2. Five red books, six green books, and four blue books are to be…

A: No. of red books=5 No. of green books=6 No. of blue books=4 The objective is to find the probability…

Q: 1. Suppose that P₁ and P₂ are probabilities on (S2, E) and that 0 s co s 1. Prove that P(A) = ∞o…

A: Given:P1 and P2 are the probabilities on Ω,ξ. 0≤∞≤1Find:P.T P(A)=∞P1(A)+∞P2(A) is also a…

Q: State whether the following statements are true or false, and provide a brief explanation. i. For a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find out the following: If A = {1,2}, then |p(p(A × p(A)))| = ?

Q: 5. Let P be a probability measure and A, B two events. Show that |P(An B) – P(A)P(B)| < . Hìnt: Show…

Q: A container contains 50 grain tokens, 20 blue tokens, and two red tokens. Two tokens are randomly…

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container. And total (35+5+3)=43…

Q: At the Skittles factory, a bag of Skittles is filled by a mechanical scoop. The scoop picks up 9,…

A: The objective of this question is to find the variance of the number of Skittles scooped up by the…

Q: A box has (4) balls. Choose (2) balls one by one with replacement, x is the first chosen and Y is…

A: Given information: No. of balls=4Selection=with replacementNo. of balls to be selected=2

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

Q: Which of the following probabilities is correct for P(C and D) if C and D are mutually exclusive?

A: It is given that The events C and D are mutually exclusive.

Q: Translate the following statements using probability notation. Use X as the random variable. The…

A: Translate the statements using probability notation.

Q: uppose that S is the set of successful students in a classroom, and that F stands for the set of…

A: Given that expression we have to find the value of

Q: 6. The prosecutor's fallacy. Let G be the event that some accused person is guilty, and 7 the event…

A: We have to show that the P(G|T)=P(T|G) iff P(G)=P(T)

Q: lex x be a random variable Xe P(x) = xex if x≥0 0 if x<o find probability that x is between 0 and 5.

A: The probability density function of the random variable X is given as follows:

Q: 4. Let X-N(6,4). Find the following probabilities a) P(X > 8) b) P(5 < X < 7) c) P(X < 3)

A: Introduction: The normal probability is a type of continuous probability distribution that can take…

Q: For any three events A, B, & D. Such that Pr(D)>0. Prove that Pr(A U B|D) = Pr(A|D) ÷ Pr(B|D) - Pr(A…

A: Given that, there are three events A, B & D. We have to prove that, Pr(A U B|D) = Pr(A|D) ÷…

Q: Suppose a € R. What are the possible values for [Q(a): Q(aº)]? Give examples with a6 EQ for each…

Q: Current Attempt in Progress Suppose that f(x) = 1.5x² for −1 -0.5) = f) Determine x such that P(x <…

Q: Suppose that an ordinary deck of 52 playing cards will be randomly ordered, and then the cards will…

A: Given information: Given that the ordinary deck consists of 52 playing cards. The cards will be…

Q: The customer service department for a company claims that 90% of all customer complaints are…

Q: The numbers a, b are positive integers. a ≤ b. Random variable X [2a,2b ] is the power of 2 in the…

A: From the given information, the numbers a and b are positive integers and a<=b. The random…

Q: Use the F table to approximate each and everyone of these probabilities. a. P(F(8,12) ≥ 2.85) =…

A: Introduction The probability shows how likely an event occurs and the value ranges from 0 to 1.

Q: 8Given that p(A | B)=0, and p(A)=.15, (a) independent? (b) exclusive? are A and B

A: we know that if two events A and B are independent thanP(A|B)=P(A)and P(B|A)=P(B) If two events A…

Q: You want the probability that an attacker without particular information must be able to crack your…

A: It is given that the prob. that a password is cracked on the first attempt is at most 12n; n=59. The…

Question

For X ∼Bin(100, 1/3 ), set up, but do not calculate, expressions that approximate
the following probabilities. The expressions must be of the form P (z1 ≤ Z ≤ z2) where
Z ∼ N (0, 1):
(a) P (30 ≤ X ≤ 35)
(b) P (90 ≤ X ≤ 100)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Do part d and e only thanks
For any two events A and B with P(B) > 0, prove that P (Aº | B) = 1 - P(A/B)
A box consists of 12 components, 5 of which are defective. (a) Components are selected and tested one at a time, without replacement, until a non-defective component is found. Let X be the number of tests required. Find P(X = 6). (b) Components are selected and tested, one at a time without replacement, until two consecutive non defective components are obtained. Let X be the number of tests required. Find P(X = 5).
A call center hires 10 call agents and owns 11 head sets for its call agents to use. Each call agent needs a head set. But the head sets are too old that they do not function well with a probability of 5%. Assume that the problem occurrence is inependent across head sets. Hint Use the following formulae Pr(X = x) = = n! = (2) p² (1 − p)²-² n! x!(n - x)! nx (n-1) x (n-2)xx2x1 and approximate (0.95)≈ 0.63, (0.95)¹0≈ 0.60 and (0.95)¹¹ ≈ 0.57. (a) Let X be the number of head sets functioning well. What are the parameters for the binomial distribution for X? (b) Calculate the expected number of head sets that function well. Do you think that the call center has enough head sets? (c) Calculate the probability that only one head set is not functioning well (d) Calculate the probability that 10 head sets or more are functioning well. (e) Calculate the probability that there are NOT enough functioning head sets. (f) Suppose that a head set is lost. Now only 10 head sets are available. Calculate…
i need in words not handwritten
assume that Pr[A] = 0.45, Pr[B] = 0.35, and Pr[A n B] = 0.25. Compute the following conditional probabilities: (1) Pr[A|B] = (2) Pr[B|A] =
What is the decision rule for this test? Select one: a. Reject Ho if (n-1) s/%o > x-1, or x-1,a c. Reject Ho if (n-1) s²/o > x²-1.x d. Reject Ho if (n-1) s/%o >x-1,1-
For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?