Approximate P(X > 102), where X is the mean of a random sample of om a Poisson(1 =100) random variable.
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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A: by bartleby policy i can gives only 1 question at a time From given : Here, x1∼N(34,100)x2∼N(30,80)…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The random variable REM sleep follows normal distribution. There are two independent samples which…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: Consider a random variable X that follows a uniform distribution with a= 1 and b = 4 Find the…
A: Answer: From the given data, a = 1 and b = 4 X follows uniform distribution,
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
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A: Given information: It is assumed that REM sleep time is normally distributed for both children and…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given : Claim : on average, children tend to have more REM sleep than adults.
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: We have given that Sample size n1= 9b, n2=9 Sample mean xbar1 =2.9 , xbar2 = 0.5 Standard deviation…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Note:Hey there! Thank you for posting the question. Since there are multiple subparts are posted,…
Q: random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given : Claim : on average, children tend to have more REM sleep than adults.
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given that x1 = 2.6 σ1 = 0.6 n1 = 8 children x2 = 1.90 σ2 = 0.5 hour n2 = 8
Q: You are to roll a fair die n = 117 times, each time observing the number of dots appearing on the…
A: I have provided the solution below please do refer it.Explanation:Solution
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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A: Given Information: Population standard deviation σ=23 Sample size n=19
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A: For children, Sample size n1 = 9, sample mean = 2.9, population SD = 0.7 For adults, Sample size n2…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given: n1=11, X1=2.5, σ1=0.6n2=11, X2=1.8, σ2=0.7α=0.01
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given: n1 = 9, x1 = 2.9, s1 = 0.7 n2 = 9, x2 = 2.2, s2 = 0.5
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A: We have given that Sample sizes n1=9 ,n2 =9 Sample means xbar1 =2.6 ,xbar2 = 1.70 and sigma1= 0.6…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The sample mean and population standard deviation for the sample of 9 children are : x1 =2.9 hrsσ1…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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- A population has a standard deviation of 34. We take a random sample of size 30 from this population. Let Xbar be the sample mean and let Xtot be the sample sum of our sample. These are random variables.a) What is the variance of this population? b) What is the variance of Xtot? (to three decimal places) c) What is the standard deviation of Xtot? (to three decimal places) d) What is the variance of Xbar? (to three decimal places) e) What is the standard deviation of Xbar? (to three decimal places) f) What is the smallest sample size, n, which will make the standard deviation of Xtot at least 900? g) What is the smallest size sample, n, which will make the variance of Xtot at least 90000You are to roll a fair die n=108 times, each time observing the number of dots appearing on the top side of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,108. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die.μXi= ____________ Enter your answer using all the decimals you can.σXi= ____________ Enter your answer using all the decimals you can. (b) What is the probability that the average topside on your tosses will be somewhere between 3.4 and 3.7? Enter your answer using all the decimals you can. _____________ (c) What is the probability that the average of your tosses is greater than 4.15? Enter your answer using all the decimals you can. ______________What is the probability of sampling a score of X = 55 or greater from a population with μ = 50 and σ = 15?
- REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that ?2 = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value…a A2 The sample of size n=87 Is drawn From a population whose standard deviation 189 Find The margin of ERROV for a 90%. Confieuence InteratREM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.5 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that σ2 = 0.7 hour. (a) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(b) Find (or estimate) the P-value. (Round your answer to four decimal places.) (c) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit
- REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that σ1 = 0.7 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that σ2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1 − μ2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value…REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that σ2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)suppose the random variable X has a normal distribution with a mean of 10 and a variance of 256 calculate the following: P(12 < x < 20 ) USE DECIMAL VALUES AND ROUND OFF FINAL ANSWER TO TWO DECIMAL PLACES!
- REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.9 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that ?2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance?State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 < ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you…REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that ?2 = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 < ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume…REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that ?1 = 0.9 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 1.60 hours per night. Previous studies show that ?2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. what is the sample test statistic find or estimate p value