7.1 A ___________ ____________ __________ is an equation used to compute probabilities of continuous random variables.
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probability density function
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7.1 True or False: The normal curve is symmetric about its mean, ?
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true
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7.1 The area under the normal curve to the right of ? equals _________.
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1/2
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7.1 The area under a normal curve can be interpreted as __________ or ____________.
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percentages or probabilities
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What tend to give rise to normal distributions?
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Summing and averaging processes; also manufacturing and biological processes
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What does area equal?
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Probability
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What are the properties of a normal distribution?
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1. Bell- shaped curve (symmetric)
2. Mean= median= mode (highest point on curve)
3. Total area under curve = 1
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What is a standard normal distribution?
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It is the you have a mean of 0 and a standard deviation of 1 (?= 0 and ?= 1)
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What are the two interpretations of area?
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1. Area to the right of __________ equals the probability that a randomly selected ________ is larger than _______.
2. Area to the right of _________ is the percentage of _________ larger than ____________.
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What is the z-score equation?
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z= (x-?)/ ?
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7.2 A random variable z that is normally distributed with mean ?= 0 and standard deviation ?= 1 is said to have the ___________ ___________ ____________.
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standard normal distribution
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7.2 The notation z? is the z-score such that the area under the standard normal curve to the right of z? is ____________.
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?
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7.2 If X is a normal random variable with mean 40 and standard deviation 10 and P (X>45) = 0.3085, then P (X< 35)= ____________.
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0.3085
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What does less than mean?
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We shade to the left of side.
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What does greater than mean?
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We shade to the right side.
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What side of the curve does the standard normal distribute chart give us the number to?
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The left side.
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7.3 A _____________ ___________ ________ is a graph that plots observed date versus normal scores.
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normal probability plot
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How can we tell if something is a normal distribution when looking at a normal probability plot?
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The points on the plot will look linear.
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How can we tell if something is not a normal distribution when looking at a normal probability plot?
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The points on the plot will make a curve
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How do we find a normal probability plot on the calculator?
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-Enter data into L1 (stat, edit)
-Turn on stat plot (2nd, y=)
-Use the bottom right chart option (L1, x-axis)
-Zoom, zoom stat (#9)
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8.1 The _________ ________ of the sample mean, x?, is the probability distribution of all possible values of the random variable x? computed from a small size of n from a population with mean ? and standard deviation ?.
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sampling distribution
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8.1 Suppose a sample size of n is drawn from a large population with mean ? and standard deviation ?. The sampling distribution of x? has mean ?x?= _____________ and standard deviation ?x?= _______________.
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x
?/ ?n
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8.1 The standard deviation of the sampling distribution of x?, ?x?, is called the ____________ ___________ of the ___________.
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standard error, mean
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8.1 True or False: The distribution of the sample mean,x?, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.
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true; if random variable x is normally distributed, the sampling distribution of the sample mean x? is normally distributed.
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8.1 True or False: The distribution of the sample mean, x?, will be normally distributed if the sample is obtained from a population that is not normally distributed, regardless of the sample size.
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false; sample size would have to be greater than 30
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8.1 A simple random sample of size n= 40 is obtained from a population with ?= 50 and ?= 4. Does the population need to be normally distributed for the sampling distribution of x? to be normally distributed? Why? What is the sampling distribution of x??
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No because n> 30; the sampling distribution of x? is normally distributed.
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What is the mean of x? (?x?) and the standard deviation of x? (?x?)?
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?x?= ?
?x?= ?/ ?n
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What does n and N stand for?
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n= sample size
N= population size
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What is the central limit theorem?
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States that x? is a normal distributed random variable is:
1. n> 30
2. x is normally distributed
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8.2 In a town of 500 households, 220 have a dog. The population proportion of dog owners in this town (expressed as a decimal) is p= __________.
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0.44 (220/500)
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8.2 The _________ ___________, denoted p?, is given by the formula p?= _________, where x is the number f individuals with a specified characteristic in a sample of n individuals.
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sample percentage
x/n
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8.2 True or False: The population proportion and sample proportion always have the same value
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false
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8.2 True or False: The mean of the sampling distribution of p? is p.
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true
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8.2 Describe the circumstances under which the shape of the sampling distribution of p? is approximately normal.
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The sampling distribution of p? is approximately normal when n ? 0.005 N and np(1-p)? 10
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What is p??
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Sample percentage
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How do you find p??
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x/ n
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How can we tell if p? is normal?
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For a binomial experiment with n trials and probability of success p, both
1. n? 0.05N
2. np(1-p) ? 10
then the random variable p? is approximately normally distributed.
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What is the mean of p? (?p?) and the standard deviation of p? (?p?)?
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?p?= P (population)
?p?=?p(1-p)/n
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9.1 A __________ _________ is the value of a statistic that estimates the value of a parameter
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point estimate
** in confidence interval for population it is p?, for confidence interval for ? it is x?
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9.1 As the level of confidence of a confidence interval increases, the margin of error ____________.
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increases
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9.1 As the sample size used to obtain a confidence interval increases, the margin of error ____________.
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decreases
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What z-score equals 90% confidence?
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1.645
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What z-score equals 95% confidence?
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1.96
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What z-score equals 99% confidence?
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2.576
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How do you write an interpretation for the confidence interval for population/ proportion p?
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We are _____ % confident that the percentage of ______________ is between ________ %and _________%.
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How do you express you answer when solving a confidence interval equation for proportion p?
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negative margin of error < p < positive margin of error
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What is the symbol for margin of error?
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E
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9.2 As the number of degrees of freedom in the t-distribution increases, the spread of the distribution _____________.
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decreases
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9.2 The notation t? is the t-value such that the area under the t-distribution to the right of t? is ____________.
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?
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9.2 True or False: To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
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false; the population does not need to be normally distributed if the sample size is sufficiently large
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How do you write an interpretation for the confidence interval of population mean?
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We are _____ % confident that population mean of ______________ is between ________(unit) and _________(unit).
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