Normal Distribution (Pinkie Length) Quiz
The question sheet
Reveal any answer as you study-
What length are you asked to measure for the pinkie length experiment?
- Your pinky finger in centimeters
- Your index finger in inches
- Your hand in centimeters
- Your thumb in millimeters
Reveal answer
Answer: Your pinky finger in centimeters
Source evidence
PDF page 390: Measure the length of your pinky finger (in centimeters).
-
In this lab, the student compares empirical data with what to reach a conclusion?
- A control group
- A random sample
- A theoretical distribution
- A frequency table
Reveal answer
Answer: A theoretical distribution
Source evidence
PDF page 390: • The student will compare empirical data and a theoretical distribution to determine if data from the experiment
PDF page 390: follow a continuous distribution.
-
Which values are used to approximate the theoretical distribution of the collected data?
- The range and IQR
- The sample mean and standard deviation
- The median and mode
- The minimum and maximum
Reveal answer
Answer: The sample mean and standard deviation
Source evidence
PDF page 391: Using your sample mean, sample standard deviation, and histogram, what was the approximate theoretical distribution of the data you collected?
-
How is the theoretical distribution written in the lab?
- X ~ N(0,1)
- X ~ (μ,σ)
- X ~ ____(____,____)
- Z ~ N(0,1)
Reveal answer
Answer: X ~ ____(____,____)
Source evidence
PDF page 391: • X ~ _____(_____,_____)
-
When completing the empirical statements, what should you do with the data first?
- Square the data
- Average the data
- Order the data
- Round the data
Reveal answer
Answer: Order the data
Source evidence
PDF page 391: Using the data you collected complete the following statements. (Hint: order the data) REMEMBER (IQR = Q3 – Q1)
-
According to the lab, IQR is calculated as:
- Q2 – Q1
- Q3 + Q1
- Q1 – Q3
- Q3 – Q1
Reveal answer
Answer: Q3 – Q1
Source evidence
PDF page 391: Using the data you collected complete the following statements. (Hint: order the data) REMEMBER (IQR = Q3 – Q1)
-
For the theoretical statements, which approximation is used?
- Normal approximation
- Uniform approximation
- Exponential approximation
- Binomial approximation
Reveal answer
Answer: Normal approximation
Source evidence
PDF page 391: Using the theoretical distribution, complete the following statements. Use a normal approximation based on the sample mean and standard deviation.
-
For a normal distribution, what is the total area under the curve?
- Two
- Zero
- Infinite
- One
Reveal answer
Answer: One
Source evidence
PDF page 392: 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.
-
The graph of the normal distribution is described as:
- Bell-shaped
- Skewed right
- Rectangular
- V-shaped
Reveal answer
Answer: Bell-shaped
Source evidence
PDF page 392: 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.
-
The distribution of z-scores is called the:
- Binomial distribution
- Uniform distribution
- Standard normal distribution
- Exponential distribution
Reveal answer
Answer: Standard normal distribution
Source evidence
PDF page 392: 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.
PDF page 392: standard normal distribution. 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 N(μ, σ) the result is the standard normal distribution Z ~ N(0,1). If this transformation is applied to any specific value x of the RV with mean μ and standard deviation σ, the result is called the z-score of x. The z-score allows us to compare data that are normally distributed but scaled differently.
-
A z-score tells you how many standard deviations a value x is from what?
- The mean μ
- The median
- The range
- The mode
Reveal answer
Answer: The mean μ
Source evidence
PDF page 392: 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.
-
Which calculator function finds a probability for a normal distribution?
- invNorm
- tcdf
- binompdf
- normalcdf
Reveal answer
Answer: normalcdf
Source evidence
PDF page 392: Standard Normal Distribution: Z ~ N(0, 1). Calculator function for probability: normalcdf (lower x z = a standardized value (z-score) value of the area, upper x value of the area, mean, standard
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
Make your own — free
Turn any notes into a game in under a minute. Free to start.