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. [br][br]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:[br]a. the probability that Amy’s time is between 37 and 44 seconds.[br]b. the probability that Amy’s time is more than 45 seconds.[br]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.[br]Note: for infinite upper boundaries, use 999, for infinite lower boundaries, use -999.