Bartolo's 1st inning fastballs in 2016 had a mean speed of µ = 89.4 mph. His pitch speeds were normally distributed, with σ = 1.7 mph.
What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?
We want the area under the curve to the RIGHT of 85.7
On your calculator:
1. Press 2nd-Vars (DISTR)
2. Choose Normalcdf( (make sure you choose CDF not PDF)
3. Your calculator will ask for the follow 4 things:
Lower Bound - The lower bound for the portion of the curve that we want the area for should be 85.7
Upper Bound - Because we want EVERYTHING above 85.7, our upper bound should be a very large number. Usually I pick something like 10000.
Mean - The mean of this distribution is 89.4
Standard Deviation - The Standard Deviation of this distribution is 1.7
4. Choose "Paste" and hit enter twice.
The number it gives you is the area under the density curve from your lower bound to your upper bound. Always check with your intuition to make sure this number seems reasonable. Remember that we estimated this number earlier.
Also remember to answer the question with a sentence: What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?
Bartolo's 1st inning fastballs in 2016 had a mean speed of µ = 89.4 mph. His pitch speeds were normally distributed, with σ = 1.7 mph.
What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?
We want the area under the curve to the RIGHT of 85.7
On your calculator:
1. Press 2nd-Vars (DISTR)
2. Choose Normalcdf( (make sure you choose CDF not PDF)
3. Your calculator will ask for the follow 4 things:
Lower Bound - The lower bound for the portion of the curve that we want the area for should be 85.7
Upper Bound - Because we want EVERYTHING above 85.7, our upper bound should be a very large number. Usually I pick something like 10000.
Mean - The mean of this distribution is 89.4
Standard Deviation - The Standard Deviation of this distribution is 1.7
4. Choose "Paste" and hit enter twice.
The number it gives you is the area under the density curve from your lower bound to your upper bound. Always check with your intuition to make sure this number seems reasonable. Remember that we estimated this number earlier.
Also remember to answer the question with a sentence: What percent of Bartolo's pitches were FASTER than the Miami Miracle pitch (85.7 mph)?
