For the past 20 years, the high temperature on April 15th has averaged = 62 degrees with a standard deviation of = 12. Last year, the high temperature was 68 degrees. Based on this information, which of the following best describes last year's temperature on April 15th?
What following?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
This may help you decide.
Far above average
To determine how last year's temperature on April 15th compares to the average, we can use z-scores.
A z-score measures the number of standard deviations an individual data point is from the mean. It provides a standardized measure that allows us to compare values from different distributions.
To calculate the z-score for last year's temperature, we can use the formula:
z = (x - μ) / σ
where:
- z is the z-score,
- x is the value we want to compare (last year's temperature),
- μ is the mean of the distribution (average temperature for April 15th),
- σ is the standard deviation of the distribution.
In this case, we have:
- x = 68 (last year's temperature),
- μ = 62 (average temperature),
- σ = 12 (standard deviation).
Plugging these values into the formula, we get:
z = (68 - 62) / 12
Simplifying, we have:
z = 6 / 12
z = 0.5
So, last year's temperature on April 15th had a z-score of 0.5.
To interpret this value, we can refer to a z-score table or use a statistical calculator. A z-score of 0.5 indicates that last year's temperature was approximately half a standard deviation above the mean.