Vocab
The shape of a normal distribution is often referred to as a _________.
Bell Curve
In a normal distribution, what percent of the data falls within one standard deviation away from the mean?
68%
For a normal distribution with a mean of 20 and a standard deviation of 4. Find the z- score for the value 14.
z = (14-20)/4
z= -1.5
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What proportion of data below 500 on the GMAT? (In context)
(All boards should include z-scores, proportions from tables, and answer in context.)
Approximately 40.52% of the scores on the GMAT exam fall under the score 500.
What is the z- score that corresponds to the 19th percentile?
z= -0.88
The greek symbols that represent the mean and standard deviation of a normal distribution are _____________.
Mean = mu
Standard Deviation = sigma
For a normal distribution with a mean of 15 and a standard deviation of 2, determine what percent of the values fall between 13 and 17.
68%
For a normal distribution with a mean of 197.18 and a standard deviation of 12.47, find and interpret the z- score for a value 221.31.
z= (221.31 - 197.18)/12.47
z= 1.94
The value 221.31 falls 1.94 standard deviations above the mean of the distribution.
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What proportion of data below 679 on the GMAT? (In context)
(All boards should include z-scores, proportions from tables, and answer in context.)
Approximately 91.31% of GMAT scores fall under the score 679.
In a normal distribution with a mean of 31 and a standard deviation of 4.6, determine the value that has a z-score of 2.18.
Set Up: 2.14 = (x-31)/4.6
Use algebra to find that z= 40.84
The percentage of values in a distribution that fall below a given value.
For a value in a normal distribution, interpret the z- score of -2.7 .
The value is 2.7 standard deviations below the mean of the distribution.
For a normal distribution with mu = 46.2.
and sigma = 9.3 , what percent of the area falls below 46.2?
50%, half of the data falls below the mean.
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What proportion of data is above 634 on the GMAT? (In context)
(All boards should include z-scores, proportions from tables, and answer in context.)
Approximately 16.85% of GMAT scores fall above the score 634.
The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a standard deviation of 16 days.
What value signifies the 85th percentile? (In context)
Approximately 85% of values fall under 282.64 days.
The mean and standard deviation of a STANDARD NORMAL Distribution.
mu = 0
sigma = 1
For a normal distribution with mean 16.7 and a standard deviation of 0.8, 99.7% of the data will fall between which 2 values?
Low Bound is 14.3
High Bound is 19.1
For a normal distribution with a mean of 20 and a standard deviation of 4. Determine the z- score and the proportion of data less than or equal to 21.3.
Show z- score, work for z- score, and proportion on board. No need for interpretation.
z=
z= (21.3-20)/4= 0.33
Proportion: 0.6293 = 62.93%
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What proportion of data is between 550 and 600 on the GMAT? (In context)
(All boards should include z-scores, proportions from tables, and answer in context.)
Approximately 15.9% of GMAT scores fall between the scores 550 and 600.
The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a standard deviation of 16 days.
What value thresholds the top 10 percent? (In context)
The value 286.48 days is the threshold for the top 10% of data.
In a normal distribution of average height in class, the mean is 65 in and the standard deviation is 5.4 in.
Interpret the standard deviation.
On average, the heights of students in class differ from the mean by approximately 5.4 inches.
For a normal distribution with a mean of 15 and a standard deviation of 2, what percent of values lie above 17?
16%
For a normal distribution with a mean of 197.18 and a standard deviation of 12.47, Determine the z- score and the proportion of data less than or equal to 172.65.
Show z- score, work for z- score, and proportion on board. No need for interpretation.
z= (172.65-197.18)/12.47= -1.97
Proportion below value: 0.0244 = 2.44%
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What proportion of data is between 410 and 520 on the GMAT? (In context)
(All boards should include z-scores, proportions from tables, and answer in context.)
Approximately 32.69% of GMAT scores fall between 410 and 520.
The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a standard deviation of 16 days.
What values make up the middle 50% of the data? (In context)
The values that make up the middle 50% of data are 255.2 days and 276.8 days.