Drinking the cereal milk? A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in their cereal bowl after they have eaten. Let p̂ be the proportion of people in the sample who drink the cereal milk. A spokesman for the dairy industry claims that 70% of all U.S. adults drink cereal milk. Suppose this claim is true.
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.
- Drinking the cereal milk? A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in their cereal bowl after they have eaten. Let p̂ be the proportion of people in the sample who drink the cereal milk. A spokesman for the dairy industry claims that 70% of all U.S. adults drink cereal milk. Suppose this claim is true.
a. Calculate the mean. (1)
b. Calculate the standard deviation. (1)
c. Justify that the sampling distribution of p̂ is approximately normal. (2)
d. Calculate the probability that at most 67% of the people in the sample drink the cereal milk. (3)
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