A fair coin is tossed 60 times. Find the probability that the head appears between 20 and 40 times by using a. binomial distribution, b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.

A fair coin is tossed 60 times. Find the probability that the head appears between 20 and 40 times by using a. binomial distribution, b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.

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: Of all freshman at a large college, 16% made the dean’s list in the current year. As part of a class…

A: Let X be the no of students who made in the list X = {0,1,2,…40} Proportion of students who made in…

Q: Determine whether the following graph can represent a variable with a normal distribution. Explain…

A: The objective is to interpret the provided graphical distribution. For this, the nature of the…

Q: new medical procedure produces side effects in 27% of the patients who receive it. In a clinical…

Q: Private nonprofit four-year colleges charge, on average, $27,919 per year in tuition and fees. The…

A: Step 1:Given the information:The mean tuition and fees μ=27,919 dollarsThe standard deviation…

Q: Using table below, find the variance for licensed dogs per household in this county? Please show…

A: X012345P(X=x)0.590.110.090.070.02

Q: Private nonprofit four-year colleges charge, on average, $26,186 per year in tuition and fees. The…

A: a. The random variable X be the cost for a randomly selected college which follows normal…

Q: Peter has collected data to find that the finishing times for cyclists in a race has a normal…

A: Given that, Mean µ=156 Standard deviation σ =15

Q: Find f0.90f0.90 for FF distribution with (22,77) degrees of freedom. f0.90=f0.90= (Round the…

A: Given that df1 = 22 , df2 = 77 P(F > f) = 0.90

Q: Private nonprofit four-year colleges charge, on average, $27,449 per year in tuition and fees. The…

Q: In the standard normal distribution, find the z value that corresponds to the 81st percentile.

A: Given, find z for 81th percentile

Q: A pharmaceutical manufacturer is concerned about the impurity concentration in batches of drug and…

Q: d. Find the 77th percentile for the mean score for this sample size. e. P(21.9204 < ữ < 22.6932) =…

A: d. The 77th percentile for the mean score for this sample size is,…

Q: CNNBC recently reported that the mean annual cost of auto insurance is 968 dollars. Assume the…

A: GivenMean(μ)=968standard deviation(σ)=259sample size(n)=36

Q: Describe the indicated sampling distribution model. this city for 5 years. Let y n Statistics from a…

Q: Private nonprofit four-year colleges charge, on average, $26,444 per year in tuition and fees. The…

A: The mean is 26,444 and the standard deviation is 6, 669.

Q: The average number of miles (in thousands) that a car's tire will function before needing…

A: given data normal distribution μ = 67σ = 17n = 49

Q: Determine whether the following graph can represent a variable with a normal distribution. Explain…

A: Solution-:We determine the given graph represents a variable with a normal distribution.Also find…

Q: Los Angeles workers have an average commute of 33 minutes. Suppose the LA commute time is normally…

A: Let, x denotes the commute time for randomly selected LA worker. It is given that- x~N33,13

Q: answer multiple choice

A: Solution If sample size becomes large than t distribution approximately equal to normal distribution…

Q: The standard deviation for this binomial distribution is

A: We have given that the random variable X that is customers order follows Binomial distribution with…

Q: 19. Sketch a normal curve for the distribution. Label the x-axis values at one, two, and three…

Q: For a measure of body weight, converted to z or standard scores, what is the probability of having…

A: Solution For standard normal distribution, Mean=0 & standard deviation = 1. Find:

Q: Determine whether the following graph can represent a variable with a normal distribution. Explain…

A: Estimating the Mean and Standard DeviationThe mean of a normal distribution is the value at the peak…

Q: Determine if the statement is true or false. In a normal distribution, about 95% of all data values…

A: we know the empirical rules…

Q: Private nonprofit four-year colleges charge, on average, $26,582 per year in tuition and fees. The…

Q: Assume the random variable X is normally distributed with mean u= 50 and standard deviation o= 7.…

A: Assume X~N(μ,σ) , where μ= 50 and σ=797th percentile ?

Q: A school gives an entry exam for admission. Suppose the score of this exam follows a normal…

A: Given that the score of the exam follows a normal distribution with a mean of 400 and a standard…

Q: Los Angeles workers have an average commute of 34 minutes. Suppose the LA commute time is normally…

A: Given information- Population mean, μ = 34 minutes Population standard deviation, σ = 14 minutes Let…

Q: > Assume the time it takes the housekeeping crew of a local hotel to clean a room varies uniformly…

Q: Guiz. 17 pis possi About 75% of all female heart transplant patients will survive for at least 3…

Q: Find the sample size necessary for an 80% confidence level with a maximal margin of error E= 0.07…

A: Given that s.d =0.34,alpha =0.2,E =0.07 ( e) n= ?

Q: (a) Use technology to determine sb1. sb1=_____? (Round to four decimal places as needed.) (b)…

A: We have used the excel data analysis tool to run the regression analysis.

Q: that x has a normal distribution with the specified mean and standard deviation. Find the indicated…

A: Given: μ=6, σ=2 The corresponding z-values needed to be computed are: Thus,

Q: In the standard normal distribution, find the z the value that corresponds to the 79th percentile.…

A: in the standard normal distribution, find the z the value that corresponds to the 79th percentile.

Q: Los Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally…

A: Let us consider, X be a random variable which is used to denote the commute of LA Angels workers…

Q: A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of…

A: The population standard deviation is unknown here. The population distribution is approximately…

Q: Describe the characteristics of the "normal distribution". Name the two parameters (two numerical…

A: A normal distribution is a symmetric Bell shaped curve having mean , median and mode all equal to…

Question

A fair coin is tossed 60 times. Find the probability that the head appears between 20 and 40 times by using
a. binomial distribution,
b. approximation of Binomial distribution by normal distribution.

Discuss why b. is better in practice.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

true or flase. the chi-square distribution, just like the normal distribution, has two parameters, mean, and standard deviation.
Find the 75th percentile of the standard normal distribution. (Round to three decimal places)
Brenda has collected data to find that the finishing times for cyclists in a race has a normal distribution. What is the probability that a randomly selected race participant had a finishing time of greater than 154 minutes if the mean is 143 minutes and the standard deviation is 11 minutes? Use the empirical rule.Provide the final answer as a percent.
CNNBC recently reported that the mean annual cost of auto insurance is 1050 dollars. Assume the standard deviation is 219 dollars, and the cost is normally distributed. You take a simple random sample of 8 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N 1050 b. What is the distribution of a? - N 1050 c. What is the probability that one randomly selected auto insurance is less than $996? 0.4013 d. a simple random sample of 8 auto insurance policies, find the probability that the average cost is less than $996. e. For part d), is the assumption of normal necessary? Yes No > Next Question 219 77.42
A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that 56 % have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the past 12 months. What is the mean and the standard deviation?
A construction company that installs drywall wanted to investigate how a person’s age affects how much dry wall they can install in a week. On one hand, it would seem that the younger workers would be able to install more, but it seems that experience would also play a role. Two random samples were taken. Assume the distributions are normal.Dry Wall Results by Age Age 18-21(sheets/week) Age 25-28(sheets/week) 92 104 109 116 93 96 81 104 115 108 109 108 84 116 121 112 94 120 116 108 a) Set up the null and alternative hypotheses to see if there is a difference in the average number of sheets of dry wall that a person can install per week based on age. b) Check the conditions. c) Calculate the test statistic. d) Find the p-value. e) Using α = 0.05, state your conclusion in the context of the problem.
In the standard normal distribution, find the z the value that corresponds to the 82nd percentile.
10 percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is 3.00 O 0.10 0.10 9.00 Clear my choice
2.) Suppose 1000 coins are tossed. Use the normal curve approximation to the binomial distribution to find the probability of getting the following result. Exactly 510 Use the table of areas under the standard normal curve. Clickv here to view page 1. Click here to view page 2. Click here to view page 3. The probability of getting exactly 510 head is (Round to four places as needed)
Sketch the distribution, show the mean and standard error, and shade the part of the curve corresponding to your calculation. Suppose that at a large university, 34% of the students decide to take their classes online. 2. Now, if the researcher takes a different sample of 1000 students, what is the probability that at least 35% of the new sample will decide to take classes online?
Please complete B & C thank you!
Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values.A bell-shaped distribution with mean 220 and standard deviation 24.The interval is to .