Z-Scores
Whats the formula for Z-score?
Z = x-m/σ
What function on the calculator is used to find the area under the curve between a lower and upper boundary?
NormalCDF
Using Inverse Norm, you're given area, but you want the ________?
Boundary.
When the z-score is given, what do you solve for to get the "score" amount?
Solve for the x.
Daily high temperatures in July are normally distribute with a mean of 85℉. What is the percentage of July days expected to be cooler than 85℉?
50%
The duration of songs on a popular music streaming platform is approximately normal with a mean of 3.8 minutes and a standard deviation of 0.6 minutes. Find the 35th percentile of the distribution of song durations?
3.56 minutes.
What is the example percentage of data that falls within +1 and -1 standard deviation of the mean in a normal distribution?
68%
SAT math scores are normal with a mean of 520 and a standard deviation of 100. What are the values for the lower, upper, mean, and standard deviation?
Lower: 600
Upper: Infinity
Mean: 520
Standard Deviation: 100
A runner marathon time yields a negative z-score. Using that context, is he faster or slower than the average participant?
Faster.
The time it takes a baker to decorate a cake is normally distributed with a mean of 60 minutes. What is the percentage that a randomly selected cake takes longer than 60 minutes to complete?
50%
Battery lifespans are normally distributed. A battery lasting 400 hours has a z-score of -1.0, and a battery lasting 500 has a z-score of +1.0. Using these values, what are the mean and standard deviation?
The mean is 450, and the standard deviation is 50.
Mr. Brandt's Honda Civic has a wide range of speeds that it can achieve, depending on traction. For many attempts the distribution of speed follows an approximately normal distribution with a mean of 80 mph and a standard deviation of 7.7 mph. What percent of the attempts will give the Civic a speed less than 68.45 mph?
6.68%
Mean = 4.16