Find P25, which is the score separating the bottom 25% scores from the top 75% scores. P25 (for single values) = Find P25, which is the mean separating the bottom 25% means from the top 75% means. P25 (for sample means) =
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A population of values has a
Find P25, which is the score separating the bottom 25% scores from the top 75% scores.
P25 (for single values) =
Find P25, which is the
P25 (for sample means) =
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- You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. A sample of 28 night students and 29 day students and their GPA's are recorded below. Test the claim using a 10% level of significance. Assume the population variances are unequal and that GPAS are normally distributed. Give answers to 4 decimal places. GPA-Night GPA-Day 3.46 3.18 2.77 2.84 3.44 3.22 3.16 3.22 3.37 3.46 2.94 3.33 2.74 2.98 3.1 3.03 2.8 3.1 3.2 3.23 3.43 3.22 3.03 3.1 3.42 3.23 2.88 3.27 2.65 2.93 3.53 3.16 3.32 3.24 2.94 3.25 2.21 3.17 2.81 2,83 2.89 3.35 2.32 3.28 2.25 3.07 3.4 3.24 2.84 3.43 3.13 3.05 2.25 2.73 2.62 2.83 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: Select an answer Select an answer H: Select an answer Select an answer Based on the hypotheses, find the following: Test Statistic- p-value- The correct decision is to Select an answer e that…You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. A sample of 24 night students and 28 day students and their GPA's are recorded below. Test the claim using a 1% level of significance. Assume the population variances are unequal and that GPAs are normally distributed. Give answers to 4 decimal places. GPA-Night GPA-Day 3.05 3.38 2.91 3.02 3.27 3.4 3.29 2.73 3.3 3.24 3.35 2.69 3.39 3.25 3.52 3.33 3.39 2.33 3.25 3.51 3.08 3.07 3.27 2.9 3.32 3.48 3 2.94 3.62 2.93 3.64 3.31 3.54 2.62 3.45 2.66 3.29 3.27 3.56 2.76 3.15 2.7 3.4 3.27 3.51 2.96 3.54 2.86 3.24 2.72 2.64 3.14 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem.H0: Select an answer x̅₂ s² x̅₁ σ² μ₂ μ₁ p ? = ≠ > < ≥ ≤ Select an answer 0 μ₂ x̅₂ x̅₁ σ² p s² μ₁ H1: Select an answer σ² x̅₂ x̅₁ μ₁ μ₂…A population of values has a normal distribution with 45.2 and a 67.7. You intend to draw a random sample of size n = 108. Please answer the following questions, and show your answers to 1 decimal place. Find the value separating the bottom 35% values from the top 65% values. Find the sample mean separating the bottpm 35% sample means from the top 65% sample means.
- 61% percent of adults in a certain country believe that life on other planets is plausible. You randomly select 5 adults and ask them whether they believe that life on other planets is plausible. The random variable represents the number of adults who believe that life on other planets is plausible. Find the mean, variance, and standard deviation of the binomial distribution for the random variable, then interpret the results. The mean= 3.85The variance= 0.89 The standard deviation= 0.94 On average, _________ out of every 5 adults in the country believe that life on other planets is plausible. In most samples of 5 adults, the number of adults who think life on other planets is plausible would differ from the mean by no more than _________.The distribution of heights in a population of women is approximately normal. Sixteen percent of the women have heights less than 62 inches. About 97.5% of the women have heights less than 71 inches. Use the empirical rule to estimate the mean and standard deviation of the heights in this population. Mean: K inches Standard Deviation: inchesUSE 3 DECIMAL A producer claims that his potato chips weight has a normal distribution at least 150 grams. The manager tries to test day shift production weight is heavier that night shift. Because of the complaints of the customers, quality control department select randomly 19 bags from the day shift and find the mean as 146 grams and variance 9 grams and randomly selected 21 bags from the night shift and find the mean as 148 grams and variance 8 grams. If manager want to test the claim as night shift mean weight of the product is greater than that of day shift at 1% level of significance. Calculate the test statistics. (H1: m night shift > m day shift).
- 34% of CSU students participate in the Statistics Games while they attend CSU. You take a random sample of 40 students. You want to determine the probability that more than 15 of them have participated in the Statistics games. Since the conditions are met, you decide to use the Normal model to find your answer. What is the mean and standard deviation of the sampling distribution?A normal distribution has a mean of µ-32 with a 4. What score separates the highest 40% of the distribution from the rest of the scores? Select one: O a. X-43 O b. X-42.67 Oc. X-33 O d. X-54.4Scores on the Math Achievement Test form a normal distribution with a mean of μ = 300 and σ = 100. A school distributes scholarships to students who score in the top 10% for this test. What score or higher must be earned to score in the top 10% on the Math Achievement Test?
- Español A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.2 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, u, is greater than 7.2 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.6 ounces and that the standard deviation is 0.5 ounces. Based on this information, complete the parts below. (a) What are the null hypothesis H. and the alternative hypothesis H, that should be used for the test? Ho :0 OEspañiol A scientist has read that the mean birth weight of babies born at full term is 7.4 pounds. The scientist has good reason to believe that the mean birth weight of babies born at full term, µ, is different from this value and plans to perform a statistical test. She selects a random sample of birth weights of babies born at full term and finds the mean of the sample to be 7.8 pounds and the standard deviation to be 1.8 pounds. Based on this information, complete the parts below. (a) What are the null hypothesis H. and the alternative hypothesis H, that should be used for the test? Ho :0 OStatistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65; 65; 70; 67; 66; 63; 63; 68; 72; 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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