Data Distribution
Normal Distribution & Z-Scores
Margin of Error
100
A teacher records the number of hours students studied for a big exam. Most students studied between 2 and 5 hours, but a small number of students studied 10–12 hours.
Is the distribution positive (right-skewed), negative (left-skewed), or approximately normal?
Positive (Right) Skewed
100
A normal distribution has mean, µ and a standard deviation, σ. Find theprobability for a randomly selected x-value from the distribution.
P(x>=mu+2sigma)
2.5%
100
A school administration estimates that between 62% and 68% of students participate in at least one extracurricular activity during the school year.
Find the sample proportion and the margin of error for the scenario.
Sample Proportion = 65%
MOE = +/- 3%
200
A gym tracks how many days per month members attend. Most members go 18–25 days, but a few members only attend 1–3 days.
Is the distribution positive (right-skewed), negative (left-skewed), or approximately normal?
Negative (Left) Skewed
200
A normal distribution has mean, µ and a standard deviation, σ. Find theprobability for a randomly selected x-value from the distribution.
P(x<=mu+sigma)
84.0%
200
A local dentist reports that between 18 and 26 patients come in for cleanings during a typical day.
Find the sample mean and margin of error for the scenario.
Sample Mean = 22 patients
MOE = +/- 4 patients
300
A high school athletic director records the number of miles each member of the cross-country team runs during a typical training week.
4, 6, 7, 5, 8, 10, 6, 9, 12, 5, 7, 8, 6, 11, 14, 7
Find the mean, standard deviation, and median. Determine if the distribution of the data (pos, neg, or normal).
Mean = 7.8
Standard Deviation = 2.7
Median = 7
Positive (Right) Skewed
300
A normal distribution has a mean of 72 and a standard deviation of 8. Find the probability that a randomly selected x-value from the distribution is between 56 and 80.
81.5%
300
A city council needs at least 70% voter approval to pass a new public transportation plan. In a recent survey, 66% of voters said they support the plan, with a margin of error of ±3% at a 95% confidence level.
Find the confidence interval.
Is the plan likely to pass?
Interval = 63% to 69%
No, the plan is not likely to pass (the interval is below the 70% needed).
400
A high school athletic director records the number of miles each member of the cross-country team runs during a typical training week.
4, 6, 7, 5, 8, 10, 6, 9, 12, 5, 7, 8, 6, 11, 14, 7
Find Min, Q1, Q3, Max, and IQR.
Min = 4
Q1 = 6
Q3 = 9.5
Max = 14
IQR = 3.5
400
A popular coffee shop experiences its busiest times on weekend mornings. During these hours, the wait times are normally distributed with a mean of 6 minutes and a standard deviation of 1.5 minutes. What is the z-score for a wait time of 8 minutes? What is the probability that the wait time is 8 minutes or more?
Z-Score = 1.33
Probability = 9.2%
400
A university reports that 64.2% of 420 randomly selected freshmen returned for their sophomore year. Using a 95% confidence level, determine the margin of error and confidence interval.
MOE = +/- 4.6%
Interval = 59.6% to 68.8%
500
A high school athletic director records the number of miles each member of the cross-country team runs during a typical training week.
4, 6, 7, 5, 8, 10, 6, 9, 12, 5, 7, 8, 6, 11, 14, 7
Create a Box and Whisper Plot for the data.
500
Researchers conduct daily counts of birds in a wildlife preserve and record the number x of birds observed each day. The counts are normally distributed with a mean of 120 birds and a standard deviation of 18 birds. What is the z-score for an x-value of 105 birds? What is the probability that no more that 105 birds are observed?
Z-Score = -0.83
Probability = 20.3%
500
A simple random sample of 500 college students shows an average increase of 3.5 hours of study time per week after attending a time-management workshop. Assume the increase in study time is normally distributed with a standard deviation of 0.8 hours. Calculate the margin of error and confidence interval for a 90% confidence level.
MOE = +/- 0.06 hrs
Interval = 3.44 hrs to 3.56 hrs