The student will compare empirical data and a theoretical distribution to determine if data from the experiment follow a continuous distribution.
Collect the data
Measure the length of your pinky finger (in centimeters).
Randomly survey 30 adults for their pinky finger lengths. Round the lengths to the nearest 0.5 cm.
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Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
Calculate the following.
= _______
s = _______
Draw a smooth curve through the top of the bars of the histogram. Write one to two complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a v-shape, does it have a hump in the middle or at either end, and so on?)
Analyze the distribution
Using your sample mean, sample standard deviation, and histogram, what was the approximate theoretical distribution of the data you collected?
X ~ _____(_____,_____)
How does the histogram help you arrive at the approximate distribution?
Describe the data
Using the data you collected complete the following statements. (Hint: order the data)
Remember
(
IQR =
Q3 –
Q1 )
IQR = _______
The 15
th percentile is _______.
The 85
th percentile is _______.
Median is _______.
What is the theoretical probability that a randomly chosen pinky length is more than 6.5 cm?
Explain the meaning of the 85
th percentile of this data.
Theoretical distribution
Using the theoretical distribution, complete the following statements. Use a normal approximation based on the sample mean and standard deviation.
IQR = _______
The 15
th percentile is _______.
The 85
th percentile is _______.
Median is _______.
What is the theoretical probability that a randomly chosen pinky length is more than 6.5 cm?
Explain the meaning of the 85
th percentile of this data.
Discussion questions
Do the data you collected give a close approximation to the theoretical distribution? In complete sentences and comparing the results in the sections titled
Describe the Data and
Theoretical Distribution , explain why or why not.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits