The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard devlation of 5.5 ounces. 16 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X- N b. What is the distribution of a? - N( c. What is the probability that one randomly selected person drinks between 15 and 17.5 ounces of coffee per day?
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.
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• Question 2
The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a
standard devlation of 5.5 ounces. 16 randomly selected people are surveyed. Round all answers to 4
decimal places where possible.
a. What is the distribution of X? X - N
b. What is the distribution of z? ī - N(d
c. What is the probability that one randomly selected person drinks between 15 and 17.5 ounces of
coffee per day?
d. For the 16 people, find the probability that the average coffee consumption is between 15 and 17.5
ounces of coffee per day.
e. For part d), is the assumption that the distribution is normal necessary? O YesO No
f. Find the IQR for the average of 16 coffee drinkers.
Q1 =
ounces
Q3 =
ounces
IQR:
ounces
Hint:
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Finding a Probability Using the Central Limit Theorem [+]
Finding Value Given a Probability Using the Central Limit Theorem [+1
The Central Limit Theorem For Sums [+]
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