Suppose the temperature of a cup of coffee is normally distributed with a mean of 142 degress F. If a cup of coffee has a z score of 1.5, which of the following is true?
None of the above.
You cannot copy and paste here. Also, if you don't know the standard deviation, you cannot determine the temperature in that cup.
Z = (score-mean)/SD
To determine which of the following statements is true, we need to understand what a z-score is and how it relates to the normal distribution.
A z-score, also known as a standard score, measures the number of standard deviations an individual value is from the mean of a distribution. It allows us to compare values from different normal distributions by transforming them into a standard normal distribution with a mean of 0 and a standard deviation of 1.
Given that the temperature of the cup of coffee is normally distributed with a mean of 142 degrees Fahrenheit, we can calculate the z-score using the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the value
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
Since the problem doesn't provide the standard deviation, we are unable to calculate the exact value of the temperature corresponding to a z-score of 1.5. However, we can make a comparison based on the z-score.
The z-score represents the number of standard deviations from the mean. A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean.
In this case, a z-score of 1.5 means that the temperature of the cup of coffee is 1.5 standard deviations above the mean. Thus, the following statement is true:
The temperature of the cup of coffee is higher than the mean temperature of 142 degrees Fahrenheit.
Keep in mind that without the standard deviation, we cannot determine the exact temperature.