IM3.7.7 Normal Distribution
Intro: What is Normal?
Which of the above distributions would you describe as “normal”?
The Normal Distribution
A swimmer named Amy specializes in the 50-meter backstroke. In competition, her mean time for the event is μ=39.7 seconds, and the standard deviation of her times is σ=2.3 seconds. Assume that Amy’s times are approximately normally distributed.
Using GGB, enter the mean and standard deviation into the probability calculator. The app will automatically fit a normal curve to your data. Use the app to find:
a. the probability that Amy’s time is between 37 and 44 seconds.
b. the probability that Amy’s time is more than 45 seconds.
c. the probability that Amy’s time would be at least 45 seconds?
With a calculator
Unfortunately, we can’t always use GGB to calculate these probabilities, but fortunately, you have a powerful calculator. To calculate these probabilities using your calculator,2ND --> VARS (DISTR) --> normalcdf( --> enter the data from the problem, press paste, then enter. Note: for infinite upper boundaries, use 999, for infinite lower boundaries, use -999.