Example 1: use of and a graphing calculator to find normal probabilities
a swimmer named amy specializes in the 50-meter backstroke. in competition, her mean time for the event is 39.7 seconds, and the standard deviation of her times is 2.3 seconds.
assume that amy’s times are approximately normally distributed.
a. estimate the probability that amy’s time is between 37 and 44 seconds.
b. using z-scores and a graphing calculator and rounding your answers to the nearest thousandth, find the probability that amy’s time in her next race is between 37 and 44 seconds.
c. estimate the probability that amy’s time is more than 45 seconds.
d. using z-scores and a graphing calculator and rounding your answers to the nearest thousandth, find the probability that amy’s time in her next race is more than 45 seconds.
e. what is the probability that amy’s time would be at least 45 seconds?
f. using z-scores and a graphing calculator and rounding your answers to the nearest thousandth, find the probability that amy’s time in her next race is less than 36 seconds.