1. Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. A. 63% of all of these types of trials are completed within how many days? (Please enter a whole number) 2. The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 76 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs. Round all answers to 4 decimal places where possible. B. The park service is considering offering a discount for 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. 3. Terri Vogel, an amateur motorcycle racer, averages 129.55 seconds per 2.5-mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: logbook of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible. C. The fastest 3% of laps are under____seconds.
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.
1. Suppose that the duration of a particular type of criminal trial is known to be
A. 63% of all of these types of trials are completed within how many days? (Please enter a whole number)
2. The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 76 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs. Round all answers to 4 decimal places where possible.
B. The park service is considering offering a discount for 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.
3. Terri Vogel, an amateur motorcycle racer, averages 129.55 seconds per 2.5-mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: logbook of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.
C. The fastest 3% of laps are under____seconds.
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