6 Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and o = V np(1 – p)3.4641. Approximate the following probabilities using the%3Dnormal approximation with the continuity correction. (Hint: 27 < x < 32 is the same as 28 < x < 31. Round your answers to four decimal places.)(a)P(x = 30)(b)P(x = 27)(c)P(x < 27)(d)P(27 < x < 32)(e)P(27 < x < 32)

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

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and o = Vnp(1 – P) = 3.4641. Approximate the following probabilities using the normal approximation with the continuity correction. (Hint: 27 < x < 32 is the same as 28

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and o = Vnp(1 – P) = 3.4641. Approximate the following probabilities using the normal approximation with the continuity correction. (Hint: 27 < x < 32 is the same as 28

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

See similar textbooks

Related questions

Q: Suppose, the walking speed of an elderly is no more than 6 km per hour. The walking speed, Y, in km…

A: Solution: From the given information,

Q: For a t-distribution with sample size 10, P (t> 1.96) z 0.0408 and P (t< -1.96) z 0.0408. Which of…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the…

A: Given, X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. We have to find…

Q: If np > 5 and nq > 5 estimate P(more than 4) with n = 13 and p = 0.5 by using the normal…

A: It is given that the value of n is 13 and p is 0.5. Conditions: np > 5 nq > 5. Checking…

Q: Q1\A/ Consider a discrete random variable X whose pmf is given by: Find: 1-E[ X ] and Var( X )? f(x)…

A: Given p.m.f. is f(x)=13 x=-1,0,1 =0 otherwise

Q: Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other…

A: From the given information, there are 13 lightbulbs. The lifetime of each is independent of each…

Q: Suppose that you have ten lightbulbs, that the lifetime ofeach is independent of all the other…

A: Given: The ten light bulbs are said to be independent of each other based on the lifetime. In which…

Q: A random sample of size n = 64, from a population with standard deviation g=9.5, is used to test…

A: Given -Sample size (n) = 64 Population standard deviation σσ = 9.5 The null and alternate hypothesis…

Q: An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise…

A: From the given information, ψx=14*2π14e-x2-4x+41024ψx2=142π14e-x2-4x+410242…

Q: Suppose again, as in Exercise 9, that a random sampleof 10 observations is taken from the normal…

A: Note : We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Suppose that X is a binomial random variable with n=300 and p=0.47 Use a normal approximation to…

Q: If Y has a binomial distribution with n trials and a probability of success p, show that the…

Q: Suppose that X is a binomial random variable with n=230 and p=0.48. Use a normal approximation to…

A: Given data, n=230 p=0.48 P(X≥100) = ?

Q: Suppose X has a gamma distribution with the following parameters: mean u- 41.5692 ms B = o /u =…

Q: Suppose you have a formula: Z = 20 + (1/2)X · Y2 Where X and Y are both random variables. Assume X…

Q: The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type…

A: Given data The number of dirt specks on a randomly selected type has a poision distribution with a…

Q: In a certain city of several million people, 7.6% of the adults are unemployed. If a random sample…

A: Given: n=230p=0.076 Normal approximation is used with mean μ=np and standard deviation σ=np1-p.

Q: According to a recent report, 68% of the population has a certain medical condition. In a random…

A: Provided data is, according to a recent report, 68% of the population has a certain medical…

Q: Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is…

Q: If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P(fewer than 4)…

Q: Suppose a quality control expert examines iterms for defects in a series of independent fixates,…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is…

Q: If np≥5 and nq≥5, estimate P(more than 6) with n=13 and p=0.3 by using the normal distribution…

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n= 200. Find the…

Q: When we consider a random sample of size n as X,,., X, which is from Binomial (n, 6). X+1 a. Is -…

A: We have given :

Q: Consider a binomial experiment with n = 20 and p = 0.4. Calculate the P(X ≥ 10). Do not use normal…

A: Given that n=20 , p=0.4 X~Binomial(n=20 , p=0.4)

Q: Based on the caterer's experience, 38% of attendees to events will prefer chicken for the main dish.…

A: We have to find standard deviation for number of successes using normal approximation of binomial…

Q: If np ≥ 5 and nq ≥ 5, estimate P(fewer than 2) with n=13 and p=0.4 by using the normal distribution…

Q: 2. Suppose that X has a hypergeometric distribution with N= 2,000, K = 800, and n= 200. Find the…

A: Hyper geometric distribution : The hypergeometric distribution may be a separate likelihood…

Q: Consider a binomial random variable x with n = 100 and p = 0.2. Use the correction for continuity…

Q: If you are given n=554n=554 and p=0.16p=0.16 for a binomial experiment, use the normal distribution…

Q: Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is…

Q: A Gamma random variable with expected value n and variance equal 2n, where n is a natural number,…

A: The parameters are estimated as follows: EX=αβ=nVX=αβ2=2nβ=VXEX=2nn=2α=n2

Q: Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is…

A: Given data: Mean = 2.61 Standard deviation = 0.76

Q: Q7. A single observation of a r.v. X having an exponential distribution (with mean 0) is used to…

A: Decision rule is given by Ho is accepted if and only if X us less than or equal to 2.

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K= 800, and n= 200. Find the…

Q: p is 0.2

A: Sample mean is an estimate of population mean Sample mean = (4+5+6)/3 = 5 here, population is…

Q: Suppose that, for a certain exam, a teacher grades on a curve. 2.2% 2.2% 34.1% 34.1% 0.1% 0.1% 13.6%…

Q: a) Evaluate α assuming that p=0.6. Use the binomial distribution. b) Evaluate β for the…

A: Given Information: Null and alternative hypothesis are, H0 : Proportion of college graduate students…

Q: A random sample of size 49 is taken from a binomial distribution with n = 60 and p = 0.4. Another…

Q: Let X denote the IQ of a randomly selected adult American. Assume, a bit unrealistically, that X is…

A: Given : Setting α, the probability of committing a Type I error, to 0.05, implies that we should…

Q: If np greater than or equals 5 and nq greater than or equals 5 , estimate P(at least 9) with n= 13…

A: Summary of this question It np is greater than or equal to 5 and nq is greater than or equals 5.

Q: If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P(at least 7) n…

A: Given, n=13 P=0.6 and q=1-p q=1-0.6=0.4 nP=13×0.6=7.8⩾5…

Q: You are given the following present value random variable for an annuity for life (x): 60aT01 if Kx…

A: Given the present value random variable for an annuity for life (x) as Z=60a10 if…

Q: If np≥5 and nq≥5, estimate P(fewer than 3) with n=13 and p=0.4 by using the normal distribution as…

A: From the provided information, Sample size (n) = 13 Probability (p) = 0.4 Now,

Q: If np≥5 and nq≥5, estimate P(more than 8) with n=11 and p=0.3 by using the normal distribution…

A: Suppose, X follows Binomial distribution with parameters n and p. If np≥ 5 and nq≥5 q=1-p, then X…

Question

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and o = V np(1 – p)
3.4641. Approximate the following probabilities using the
%3D
normal approximation with the continuity correction. (Hint: 27 < x < 32 is the same as 28 < x < 31. Round your answers to four decimal places.)
(a)
P(x = 30)
(b)
P(x = 27)
(c)
P(x < 27)
(d)
P(27 < x < 32)
(e)
P(27 < x < 32)

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)
1) A producer of soft drinks was fairly certain that her brand had a 15% share of the soft drink market. In a market survey involving 3000 consumer of soft drinks, 250 expressed a preference for her brand. If the 15% figure is correct, find the probability of observing 400 or more consumers who prefer her brand of soft drink. [Hint: Use normal approximation and z-value must be rounded-off to 2 decimal places only
Consider a binomial random variable x with n = 100 and p = 0.2. Use the correction for continuity and approximate P(x ≤ 31)using the normal approximation. (Round your answer to four decimal places.) P(x ≤ 31) =
According to a recent report, 27% of the population has a certain medical condition. In a random sample of n=210 from this population, what is the probability at most 24.3% of the sample will have the medical conditions. P(p̂ ≤ 0.243) = _________________ use normal approximation Note: The population is very large, and a sample of n=210 represents far less than 0.01% of the entire population.
Suppose that you have ten lightbulbs, that the lifetime ofeach is independent of all the other lifetimes, and that eachlifetime has an exponential distribution with parameter l.a. What is the probability that all ten bulbs fail beforetime t?b. What is the probability that exactly k of the ten bulbsfail before time t?c. Suppose that nine of the bulbs have lifetimes that areexponentially distributed with parameter l and thatthe remaining bulb has a lifetime that is exponentiallydistributed with parameter u (it is made byanother manufacturer). What is the probability thatexactly five of the ten bulbs fail before time t?
let x denote the number of failures before the third success in a sequence of independent and identical Bernoulli trials. Given a simple random sample of (4,5,6) to estimate the probability of success p, which statement is true? a. the method of moment estimate of p is 0.167 b. p is 0.2 c. cannot be estimated d. p is 0.375
If no is greater than or equal to 5, estimate P(fewer than 5) with n=14 and P=0.5 by using the normal distribution as an approximation to the binomial distribution; if np<5 or no<5, then state that the normal approximation is not suitable.
If np(is greater than or equal to)5, estimate P(fewer than 5) with n=13 and p=0.4 by using the normal distribution as an approximation to the binomial distribution; if np<5 or nq<5, then state that the normal approximation is not suitable. P(fewer than 5)=?