93% of students in Mr. Adkins AP statistics class turn in their assignments on time, 85% of Mr. Adkins AP statistics students turn in their assignments with every problem completed, and 80% of Mr. Adkins AP statistics students turn in their assignments on time and with every question completed. Assume that assignment submissions are independent. (a) Given that a randomly selected assignment is turned in late, what is the probability that every problem was completed? (b) If Mr. Adkins randomly selects student assignments one at a time, what is the probability that the first assignment he finds that is not turned in on time with every question completed is one of the first 5 selected? (c) Mr. Adkins has 70 total AP statistics students. Describe the distribution of the proportion of papers that are turned in complete and on time for a randomly chosen assignment. (d) Explain how you would conduct a simulation to estimate the probability that at least 68 of Mr. Adkins 70 AP statistics students would turn an assignment in on time.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
93% of students in Mr. Adkins AP statistics class turn in their assignments on time, 85% of Mr. Adkins AP statistics students turn in their assignments with every problem completed, and 80% of Mr. Adkins AP statistics students turn in their assignments on time and with every question completed. Assume that assignment submissions are independent.
(a) Given that a randomly selected assignment is turned in late, what is the probability that every problem was completed?
(b) If Mr. Adkins randomly selects student assignments one at a time, what is the probability that the first assignment he finds that is not turned in on time with every question completed is one of the first 5 selected?
(c) Mr. Adkins has 70 total AP statistics students. Describe the distribution of the proportion of papers that are turned in complete and on time for a randomly chosen assignment.
(d) Explain how you would conduct a simulation to estimate the probability that at least 68 of Mr. Adkins 70 AP statistics students would turn an assignment in on time.
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