How many standard deviations away from the mean must you go to capture 68% of the area under the normal curve? Round to 2 decimal places (i.e., don't use the Empirical Rule).

Q: In a regional high school swim meet, women’s times (in seconds) in the 200-yard freestyle ranged…

A: Obtain the value of standard deviation, using the Empirical Rule.   The value of standard deviation,…

Q: If a normal distribution has a mean of 28.0 and a standard deviation of 2.5, what is the value of…

A: Given information Mean µ = 28 Standard deviation σ = 2.5 Using standard normal table,

Q: How heavy a load, in pounds, is needed to pull apart pieces of Douglas fir 4 in. long and 1.5in.…

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Q: A quantitative data set of size 150 has mean 35 and standard deviation 4. At least how many…

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Q: A normal distribution has a mean of 90 and a standard deviation of 9. Find the z-score for a data…

A: Solution: Let X be the data value. From given information, X has mean µ=90 and a standard deviation…

Q: A quantitative data set of size 200 has mean 20 and standard deviation 4. At least how many…

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Q: A quantitative data set of size 80 has mean 30 and standard deviation 5. At least how many…

A: Given information- Sample size, n = 80 Mean, μ = 30 Standard deviation, σ = 5 We have to find the…

Q: Imagine that scores for national aptitude exam have a normal distribution with a mean of 700 a…

A: Given: Mean = 700 Standard deviation = 30 Let X ~ N(700, 302)

Q: The human population has a mean IQ score of µ = 100 and a standard deviation of σ = 15. Find the…

A: From the given information, µ = 100 and σ = 15.

Q: A population has a standard deviation ? of 18.8 units. (Give your answers correct to two decimal…

A: Given: Population standard deviationσ=18.8 Sample size(n)=105   Formula for standard error(SE) SE=σn

Q: According to the empirical rule, approximately what percentage of the area under a normal…

A: The empirical rule, also referred to as the three sigma rule or 68-95-99.7 rule, Empirical rule is…

Q: According to the empirical rule, approximately what percentage of the area under a normal…

A: The empirical rule is based on the normal distribution which shows the area under the normal curve…

Q: In a normal distribution with a mean of 72 and a standard deviation of 12 what is the value of x at…

A: A normal distribution is also called Gaussian distribution which has bell shaped curve. The normal…

Q: 16.)Find the percent of the area under a normal curve between the mean and the given number of…

A: Since z-value for mean is 0. So the area under a normal curve between the mean and the given number…

Q: A normal distribution has a mean of 126 and a standard deviation of 10. Find the z-score for a data…

A: The random variable X follows normal distribution. The population mean is 126 and population…

Q: A population on N=8 scores has a standard deviation of 3. what is the value of SS, the sum of the…

A: Obtain the value of SS, the sum of the squared deviations, for this population. The value of SS, the…

Q: Assume that the amount of time a person experiences cold virus symptoms are normally distributed…

A: Given data Mean = 7.5 days  Standard deviation  = 1.5d days To find: What proportion of cold…

Q: A normal distribution has a mean of 103 and a standard deviation of 5. Find the z-score for a data…

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Q: A quantitative data set of size 87 has mean 80 and standard deviation 10. At least how many…

A: To obtain standard deviation distance from mean to 100,

Q: Apply Chebyshev’s rule to solve. A quantitative data set of size 150 has mean 35 and standard…

A: Chebyshev’s rule: The Chebyshev’s rule states that, for any quantitative data set and any real…

Q: A normal distribution has a mean of 106 and a standard deviation of 9. Find the z-score for a data…

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Q: Assuming a standard deviation of 0.015 and an approximate normal distribution, how large a sample is…

A: Given : Margin of error, ME = 0.05 population standard deviation, σ = 0.015…

Q: Sketch a normal distribution/bell curve with a mean of 60 and a standard deviation of 20.  What…

A: Given that  X~Normal( μ=60 , σ=20 )

Q: A population has a standard deviation ? of 18.1 units. (Give your answers correct to two decimal…

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Q: For a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of…

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Q: A quantitative data set of size 80 has mean 30 and standard deviation 6. Approximately how many…

A: From the provided information, Population size (N) = 80 Mean (µ) = 30 Standard deviation (σ) = 6 X~N…

Q: Apply Chebyshev’s rule to solve. A quantitative data set of size 80 has mean 30 and standard…

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Q: The human population has a mean IQ score of µ = 100 and a standard deviation of σ = 15. Find the…

A: The normal distribution is the most useful theoretical distribution for continuous variables.…

Q: A quantitative data set of size 70 has mean 35 and standard deviation 5. At least how many…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: A normal distribution has a mean of 144 and a standard deviation of 8. Find the z-score for a data…

A: Given that, μ=144, σ=8 We know that, z-score is given as, Z=X-μσ

Q: The age at which babies walk is normally distributed with a mean of 13 months with a standard…

A: From the provided information, Mean (µ) = 13 months Standard deviation (σ) = 1.5 months Let X be a…

Q: Assuming the distribution of the above scores is normal, the percentage o people who scored within 1…

A: Let z be the random variable follows normal distribution

Q: What percentage of the area under the normal curve is within +/-1, +/-2, and +/-3 standard…

A: Let Z be the random variable from standard normal distribution with mean = 0 and standard deviation…

Q: The amount of Derek's monthly phone bill is normally distributed with a mean of $74 and a standard…

A: By Empirical Rule: 68% of the values lie between 1 standard deviation of the mean, thus:…

Q: What is the standard deviation? (Round off to two decimal places if necessary)

A: Calculate Standard deviation  from the following…

Q: A normal distribution has a mean of 117 and a standard deviation of 4. Find the z-score for a data…

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Q: A nurse at a local hospital is interested in estimating the birth weight of intants. How large a…

A: CL = 98% Error, E = 2 ounces Standard Deviation,σ = 5 ounces

Q: How large a sample must be taken to be 99% confident that the estimate of the average time of…

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Q: Suppose that the time spent by children under the age of 12 in front of a screen per year has the…

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Q: Under which circumstance is a score that is located 5 points above the mean a central value that is…

A: Answer : If you want the point to be relatively close to the mean then the standard deviation should…

Q: A normal distribution has a mean of 130 and a standard deviation of 10. Find the z-score for a data…

A: We have given that,  Let X be the random variable from normal distribution with mean (μ) = 130 and…

Q: Find the mean, variance, and standard deviation for the number of heads when 20 coins are tossed.…

A: Let n be the number of coins tossed = 20 Let p be the probability of getting head = 0.5 Let X denote…

Q: A normal distribution has a mean of 108 and a standard deviation of 5. Find the z-score for a data…

A: Given, Mean, μ=108 Standard deviation, σ=5 z-score for a data x is calculated by using the formula…

Q: A normal distribution has a mean of 147 and a standard deviation of 4. Find the z-score for a data…

A: Standardized z-score:   The standardized z-score represents the number of standard deviations the…

Q: A company manufactures snow shovels in batches of 53 and there is a 15% rate of defects. Round all…

A: Given that a company manufacturers  snow shovels in batches of 53 and there is a 15% rate of…

Q: A normal distribution has a mean of 105 and a standard deviation of 7. Find the z-score for a data…

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Q: A normal distribution has a mean of 136 and a standard deviation of 10. Find the z-score for a data…

A: Given information- Population mean, µ = 136 Population standard deviation, σ = 10 We have to find…

Q: A random sample of 100,000 credit sales in a department store showed an average sale of $87.25. From…

A: Given,sample size(n)=100,000population standard deviation(σ)=$20.00mean(x¯)=$87.25

Q: How large a sample must be taken to be 99% confident that the estimate of the average time of…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.