Z-scores
What is the Z-Score formula?
Z= x-mean/standard deviation
What goes in the parenthesis? normalcdf (__,__,__,__)
lower, upper, mean, standard deviation
What goes in the parenthesis? InvNorm (___,___,___)
area, mean, standard deviation
What does cdf mean in normalcdf?
Cumulative Distribution Function
You already have the area, so what are you using InvNorm to find?
the boundary
If a data point is 2.5 standard deviations below the mean, what is its Z-score?
-2.5
The distribution of wait times at a doctor is normally distributed with a mean of 30 minutes and a standard deviation of 4.3 minutes. What percent of the wait times is less than 25 minutes?
12.2%
The distribution of wingspans for a certain hawk species is normally distributed with a mean of 49 inches and a standard deviation of 3.5 inches. If a wingspan is at the 97th percentile, what is the hawk's wingspan, in inches?
55.58 inches
A local bread delivers bread to cafes every morning. The delivery times are normally disturbed with a mean of 45 minutes and a standard deviation of 5 minutes. A certain delivery takes 40 minutes. What is its Z-score?
1
The distribution of speed is normally distributed with a mean of 80 mph and a standard deviation of 7.7 mph. What percent of attempts will have a speed greater than 85 mph?
25.8%
The diameters of grapefruits grown in a Florida orchard are approximately normally distributed with a mean of 4.5 inches and a standard deviation of 0.4 inches. The middle 50% of grapefruits at this orchard fall between which two diameter lenghts?
4.23 inches, 4.77 inches
Two friends are comparing their test results. Friend 1 was at the 40th percentile and Friend 2 had a Z-score of -0.218. Which friend performed better?
After accelerating for 20 seconds from a stop, a DeLorean sports car 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 DeLorean a speed less than 68.45 mph? 9.25% is an ESTIMATE, get the EXACT answer
6.68%
The distribution of distances traveled by paddle boarders is normally distributed with a mean of 2.8 and a standard deviation of 0.5. Find the distances at the 20th and 80th percentiles.
2.38 inches, 3.22 inches