**Title: Understanding the Normal Approximation to the Binomial Distribution****Description:** This lesson will explore whether the normal distribution can approximate the binomial distribution in specific scenarios. We will analyze given data, perform necessary calculations, and discuss how to sketch applicable graphs. The process involves determining the circumstances under which normal approximation is suitable, and when it is not, we employ the binomial distribution to calculate required probabilities.### Problem Statement**Scenario:**In a survey of U.S. college students, 62% said that if their college offers new programs tailored to the new economy, it will make them more likely to re-enroll. You randomly select 41 college students.**Tasks:**1. Determine the probability that the number who are more likely to enroll if their college offers new programs tailored to the new economy is: - **Exactly 25** - **At least 30** - **At most 24**### Steps to Determine the Utilization of Normal Distribution:1. **Check the Conditions:** - The normal distribution can be used to approximate the binomial distribution when both $ np $ and $ n(1-p) $ are greater than or equal to 5. Here: - $ n = 41 $ - $ p = 0.62 $ Calculate: - $ np = 41 \times 0.62 = 25.42 $ - $ n(1-p) = 41 \times 0.38 = 15.58 $ Both values are greater than 5, so we can use the normal approximation.2. **Normal Approximation:** - Mean ($ \mu $) of the binomial distribution: $ \mu = np = 25.42 $ - Standard deviation ($ \sigma $) of the binomial distribution: $ \sigma = \sqrt{np(1-p)} = \sqrt{25.42 \times 0.38} = \sqrt{9.6596} \approx 3.11 $3. **Convert to Z-Scores and Find Probabilities:** - For **exactly 25**: - Use continuity correction: $ P(24.5 < X < 25.5) $ - Convert to Z-scores: \( Z = \frac{24.5 - 25.

Binomial distribution tends to Normal distribution if n>30

Answered: Determine whether you can use a normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A survey asks questions about one's happiness and health. One would think that health plays a role in one's happiness. Use the data in the accompanying table to determine whether healthier people tend to also be happier. Treat level of health as the explanatory variable. E Click the icon to view the data table. Create a conditional distribution for the data. Level of Health Data table Level of Happiness Not too happy Poor Fair Good Excellent Poor Fair Good Excellent Pretty happy Not too happy Pretty happy Very happy 1,376 1,629 9,642 696 732 Very happy 950 3,817 5,185 345 1,372 4,520 5,085 Total (Round to three decimal places as needed.) Print Done
Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 600 adults and ask them to name their favorite sport. Complete parts (a) through (d). Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. No, because ng < 5. O B. Yes, because both np25 and ng 25. O C. No, because np <5. (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 56. |(Round to four decimal places as needed.)
Read the following passage and observe the word length of each word. Make a frequency distribution of word length. Pargraph: “Statistics play an intrinsic role in computer science and vice versa. Statistics is used for data mining, speech recognition, vision and image analysis, data compression, artificial intelligence, and network and traffic modeling. A statistical background is essential for understanding algorithms and statistical properties that form the backbone of computer science. Typically, statistical approach to models tends to involve stochastic (random) models with prior knowledge of the data. The computer science approach, on the other hand, leans more to algorithmic models without prior knowledge of the data. Ultimately, these come together in attempts to solve problems.” Note table should neat and clean
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below O A. The statement is false. A sampling distribution is never normal. O B. The statement is false. A sampling distribution is normal only if n230. O C. The statement is true. O D. The statement is false. A sampling distribution is normal if either n230 or the population is normal. Click to select your answer. ... acer
A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether this distribution has changed, you randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the claimed or expected distribution? Use a=0.10. Complete parts (a) through (d). New Survey Frequency, f 111 97 Response Old Survey % Rewards 29% 23% Low rates Cash back Discounts Other 22% 108 8% 46 18% 63 UD. XX O D. X Xo 2 OC. X >Xo OC. X>x (c) Calculate the test statistic. (Round to three decimal places as needed.) %3D (d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. V the claimed or ▼enough evidence to conclude that the distribution of motivations Ho At the 10% significance level, there expected distribution.
1. What is a random variable? Give an example. Suppose you are shopping online for a new toy for your dog. As you look at the product reviews, you see the following distribution of ratings. Use this table for questions 2-5. Stars Frequency 6. 4 3 3 1 1 2. Sketch a data visualization of the distribution of stars. 3. What is the probability that a randomly chosen reviewer gave the dog toy 3 stars? What is the probability that a randomly chosen reviewer gave the dog toy 3 or fewer stars?
The expected value of the mean is: The mean of the true population means The mean of the standard errors of the mean. The mean of the random sampling errors. The mean of the sampling distribution of the mean.
determine whether the given procedure results in a binomial distribution. if not, give the reason. Rolling a single die 34 times, keeping track of the number of 3s that are rolled.
Determine whether the given procedure results in a binomial distribution. Tossing a coin 25 times and recording the number of tails you get.
Determine whether the given procedure results in a binomial distribution. Tossing a coin 12 times and recording the number of outcomes that are heads.
Q4: The mean of a distribution is 23, the median is 24, and the mode is 25.5. It is most likely that the distribution is A. symmetrical. B. negatively skewed. C. positively skewed. D. none of the above.
Provide an appropriate response. A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: $10.00 $12.50 Price Probability 0.25 0.3 $15.00 0.45 Suppose the mean cost of the rats turned out to be $13.00 per week. Interpret this value. O The average cost for all weekly rat purchases is $13.00. O The median cost for the distribution of rat costs is $13.00. O The rat cost that occurs more often than any other is $13.00. O Most of the weeks resulted in rat costs of $13.00.

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