Normal Distribution (Pinkie Length) Quiz
The question sheet
Reveal any answer as you study-
In the pinkie length experiment, what is measured and in what unit?
- Finger circumference in mm
- Pinkie finger length in centimeters
- Arm length in meters
- Hand width in inches
Reveal answer
Answer: Pinkie finger length in centimeters
Source evidence
PDF page 405: Measure the length of your pinkie finger, in centimeters.
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What theoretical probability is requested for pinkie lengths?
- That a length is less than 5 cm
- That a length equals the mean
- That a length is exactly 6.5 cm
- That a length exceeds 6.5 cm
Reveal answer
Answer: That a length exceeds 6.5 cm
Source evidence
PDF page 406: • What is the theoretical probability that a randomly chosen pinkie length is more than 6.5 cm?
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According to the text, how is the IQR reminder given?
- IQR = max – min
- IQR = Q1 – Q3
- IQR = Q2 – Q1
- IQR = Q3 – Q1
Reveal answer
Answer: IQR = Q3 – Q1
Source evidence
PDF page 406: Using the data you collected complete the following statements. Hint—Order the data. REMEMBER (IQR = Q3 – Q1)
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What is the notation for the normal distribution?
- X ~ Exp(m)
- X ~ N(μ, σ)
- X ~ U(a, b)
- X ~ B(n, p)
Reveal answer
Answer: X ~ N(μ, σ)
Source evidence
PDF page 407: normal distribution a continuous random variable (RV) where μ is the mean of the distribution and σ is the standard
PDF page 407: deviation; notation: X ~ N(μ, σ). If μ = 0 and σ = 1, the RV is called the standard normal distribution.
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What does the z-score tell you about a value x?
- The total area under the curve
- How many standard deviations x is from μ
- Its raw frequency
- The population size
Reveal answer
Answer: How many standard deviations x is from μ
Source evidence
PDF page 407: A z-score is a standardized value. Its distribution is the standard normal, Z ~ N(0, 1). The mean of the z-scores is zero and the standard deviation is one. If z is the z-score for a value x from the normal distribution N(μ, σ), then z tells you how many standard deviations x is above—greater than—or below—less than—μ.
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When X follows the standard normal, how is it often noted?
- Z ~ N(0, 1)
- Z ~ U(0, 1)
- X ~ N(1, 0)
- X ~ B(0, 1)
Reveal answer
Answer: Z ~ N(0, 1)
Source evidence
PDF page 407: standard normal distribution a continuous random variable (RV) X ~ N(0, 1); when X follows the standard normal distribution, it is often noted as Z ~ N(0, 1). x – μ z-score the linear transformation of the form z = ; if this transformation is applied to any normal distribution X ~ σ
PDF page 407: Standard Normal Distribution: Z ~ N(0, 1). Calculator function for probability: normalcdf (lower x Z ~ N(0, 1) value of the area, upper x value of the area, mean, standard z = a standardized value (z-score) deviation)
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Since the normal is continuous, the total area under its curve is:
- one
- infinite
- zero
- the mean
Reveal answer
Answer: one
Source evidence
PDF page 407: The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bellshaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution, is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
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The graph of the normal distribution is described as:
- V-shaped
- J-shaped
- bell-shaped
- rectangular
Reveal answer
Answer: bell-shaped
Source evidence
PDF page 407: The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bellshaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution, is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
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Which calculator function gives a normal probability?
- tcdf
- normalcdf
- invNorm
- binompdf
Reveal answer
Answer: normalcdf
Source evidence
PDF page 407: Standard Normal Distribution: Z ~ N(0, 1). Calculator function for probability: normalcdf (lower x Z ~ N(0, 1) value of the area, upper x value of the area, mean, standard z = a standardized value (z-score) deviation)
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Which calculator function finds the k percentile of a normal distribution?
- invNorm
- normalcdf
- tcdf
- invT
Reveal answer
Answer: invNorm
Source evidence
PDF page 407: Calculator function for the k percentile: k = invNorm (area
PDF page 407: To find the k percentile of X when the z-score is known, to the left of k, mean, standard deviation)
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For a value x below the mean, its z-score is:
- negative
- positive
- zero
- undefined
Reveal answer
Answer: negative
Source evidence
PDF page 407: A z-score is a standardized value. Its distribution is the standard normal, Z ~ N(0, 1). The mean of the z-scores is zero and the standard deviation is one. If z is the z-score for a value x from the normal distribution N(μ, σ), then z tells you how many standard deviations x is above—greater than—or below—less than—μ.
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For NBA heights (μ=79, σ=3.89), a height of 85 inches gives what interpretation?
- 1.54 std deviations below the mean
- exactly at the mean
- 4 std deviations above the mean
- 1.54 std deviations above the mean
Reveal answer
Answer: 1.54 std deviations above the mean
Source evidence
PDF page 418: b. Use the z-score formula. z = 1.5424. The height 85 inches is 1.5424 standard deviations above the mean. An NBA
PDF page 418: player whose height is 85 inches is taller than average.
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