1. Recall that a normal distribution should be able to spread approximately three standard deviations from the mean value and that the mean and variance of a Poisson distribution are equal. What minimum value should n *λ take on to ensure that the sampling distribution for the sample mean from a Poisson(2) distribution will be approximately normal?
Q: For a population that has a standard deviation of 10, figure the standard deviation of the…
A: Given that Population standard deviation =10 Then we have to find the standard deviation of the…
Q: a)Determine the mean of sample means distribution b) Determine the standard deviation (standard…
A: The objective of the question is to determine the mean and standard deviation of the sample means…
Q: size
A: As per the weak law of large numbers, every distribution tends to normal distribution as we increase…
Q: Past data reveals that such gestation periods have a mean of 65 days with standard deviation 20days.…
A: Given data: The gestation period of wolves (X) is normally distributed with mean and standard…
Q: A simple random sample of size 17 is taken from a population with unknown standard deviation. A…
A: The following assumptions are required for the small sample confidence interval about mean to be…
Q: 5. A manufacturer claims that the mean tensile strength of thread A exceeds the average tensile…
A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
Q: A science teacher claims that the mean scores on a science assessment test for girls are equal. The…
A: Given that Sample sizes n1=18 , n2=20 Sample means x1=153 , x2=149 Standard deviation s1=23 ,…
Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…
A: L
Q: Suppose x has a normal distribution with mean u = 42 and standard deviation o = 13. Describe the…
A: Mean of the sampling distribution of the sample mean. Standard deviation of the sampling…
Q: A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96%…
A: To find the confidence interval for the variance, we need to use the Chi-squared distribution. The…
Q: fo (b) What is the mean and standard deviation of the sampling distribution of x assuming u = 4 and…
A: Given that Sample size n =40 Population mean μ =4 Population standard deviation =2
Q: Response to allergen inhalation in allergic primates. In a study of 12 monkeys, the standard error…
A: From the provided information, Sample size (n) = 12 Standard error (SE) = 0.4
Q: In a recent SAT, the mean score for all examinees was 1020. Assume that the distribution of SAT…
A:
Q: The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million…
A: We have given that Sample sizes n1= 40 , n2= 35 Sample means xbar1= 3.2 , xbar2=1.9 Standard…
Q: How does a sample size affect how close a normal distribution of either sample means or sample…
A: As per Central limit theorem, the sampling distribution of sample mean or sample proportion follow…
Q: When simple random samples are drawn from a population that is normally distributed, the sampling…
A: According to the definition of Central limit theorem, the sampling distribution of the sample means…
Q: 1. A normal distribution is informally described as a probability distribution that is "bell-shaped"…
A:
Q: The annual per capita consumption of red meat in the U.S. is normally distributed with a mean of…
A: From the given information : n = 50 mean = 85.6 standard deviation = 20.5
Q: A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal…
A:
Q: The median ACT scores for four-year colleges to follow normal distribution with a mean of 24 points…
A:
Q: 7. An education analyst believes that the average SAT scores for women exceed the average SAT scores…
A: From the provided information,
Q: A biologist studies the gestation period of wolves. Past data reveals that such gestation periods…
A: Concept of sampling distribution of sample mean:Let a particular characteristic of a population is…
Q: The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million…
A: The sample standard deviations are s1=2 and s2=1.5.
Q: The shape of the T-distribution curve is wider than the normal curve because, O a. it has more…
A: If population standard deviation is known and large sample size i.e, n > 30 then we use z-…
Q: Can a normal approximation be used for a sampling distribution of sample means from a population…
A:
Q: According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015…
A: The question is about central limit theoremGiven :Popl. mean life expectancy ( ) = 79.3 yearsPopl.…
Q: It is known that under ordinary conditions, 15% of people will not contract a certain disease.…
A: Obtain the mean of the normal distribution. The mean of the normal distribution is obtained below…
Q: Recall that a normal distribution should be able to spread approximately three standard deviations…
A: Here we are given that the mean and variance of a Poisson distribution are equal. Here we are…
Q: When do we use z-distribution? A.) when the standard deviation is unknown. B.) when the population…
A: As per our guidelines we are supposed to answer only one question per post so I am solving first…
Q: listribution of age at death, X, is not normal because it is skewed to the left. I all possible…
A: u = 71.8 s = 15 n = 100 z = 2.33
Q: 12. The red blood cell count for a population of adult males can be approximated by a normal…
A: GivenMean(μ)=5.4variance(σ2)=0.16standard deviation(σ)=0.16=0.4
Q: Suppose that the rice mill wants to test its product to find out whether it meets the average weight…
A: We have given that, the average weight of rice of 50 kilograms with a standard deviation of 0.18…
Q: Suppose that the sampling distribution of size 10 has a mean of 30 and standard deviation of 3.…
A:
Q: If x has a normal distribution with mean u=15 and standard deviation o=3, describe the distributin…
A: Given information, μ=15σ=3 Given sample sizes, n=4, n=16, n=100. The sampling distribution for n=4:…
Q: Assume that stock fund expenses and municipal bond fund expenses are each approximately normally…
A:
Q: Assume that stock fund expenses and municipal bond fund expenses are each approximately normally…
A: Given that, n1=25, x1=1.15, s1=0.31n2=25, x2=0.35, s2=0.15 The critical value at 0.05 level of…
Q: Prove that for any discrete distribution, standard deviation is not less than mean deviation from…
A:
Q: A biologist studies the gestation period of wolves. Past data reveals that such gestation periods…
A: Obtain the mean of the sampling distribution of sample mean for a sample of size 15. The mean of the…
Q: Suppose that for a random sample of 250 firms that revalued their fixed assets, the mean ratio of…
A:
Given information:
Normal distribution should be able to spread approximately three standard deviations from the mean value and the mean and variance of a Poisson distribution are equal.
Step by step
Solved in 2 steps
- An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).Suppose that for a random sample of 250 firms that revalued their fixed assets, the mean ratio of debt to tangible assets was 0.629, and the sample standard deviation was 0.177. For an independent random sample of 450 firms that did not revalue their fixed assets, the mean ratio of debt to tangible assets was 0.599, and the sample standard deviation was 0.163. Assuming that the population distributions are normal with equal variances, find a 95% confidence interval for the difference between the two population means. E Click the icon to view a table of upper critical values of Student's t distribution. A 95% confidence interval for the difference between the two population means is (Round to four decimal places as needed.)Can a normal approximation be used for a sampling distribution of sample means from a population with u = 36 and a = 6, when n - 49? Answer Tables Кeypad Keyboard Shortcuts O No, because the standard deviation is too small. O No, because the sample size is more than 30. O Yes, because the mean is greater than 30. O Yes, because the sample size is at least 30.
- 2. The general weighted average of Mechanical Engineering students from a certain class are approximately normally distributed with mean 1.65 and standard deviation of 0.9. What must their general weighted average be if they want to be in the 1%, 5% and 10% of the class respectively?What important theorem in statistics implies that, for a large sample size, the possible sample proportions of that size have approximately a normal distribution?a)Determine the mean of sample means distribution b) Determine the standard deviation (standard error) of sample means distributionc) Draw a Normal (bell-shaped) graph for sample means distribution byhand on a paper showing x and y axes without any values marked on them. However,label the values of mean and standard deviation as described below. The adult male heights in a country vary normally with mean of 70 inches and standarddeviation of 4 inches. We draw many samples of size 100 from the above populationusing repeated random sampling and record the mean height for each sample to constitutea sample means distribution (?̅ -distribution). Do the above for the distribution.
- 4. Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation = 2.4%. A random sample of 19 Australian bank stocks has a sample mean of = 8.71%. For the entire Australian stock market, the mean dividend yield is = 5.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9% ? Use Q=.05. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis? A. The p-value is less than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis. B. The p-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis. C. The p-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the…5. The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimcters. Assume the distributions of both types of breeds are normally distributed. (n) Suppose we are taking a random sample of 64 terriers. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 61 terriers excoedls 75 centimetcrs. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers excoeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.Assume all populations are normally distributed. A travel analyst claims that the mean price of a round trip flight from New York City to Los Angeles is less than $507. In a random sample of 55 round trip flights from NYC to LA, the mean price is $502. Assume the population standard deviation is $111. At α = 0.05, is there enough evidence to support the travel analyst’s claim?