Amy swims the 50-m backstroke. When in competition, her mean time is 39.7 seconds. And the standard deviation is 2.3 seconds. If she needs to swim faster than 37 seconds to earn a medal, what is the probability that she earns a medal? (Hint - use your normal distribution chart)

And we can find this probability we can use this formula:

And using the normal standard distribution table or excel and we got:

Step-by-step explanation:

Let X the random variable that represent the time so complete the 50 m of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

We can use the z score formula given by:

If we apply this formula to our probability we got this:

And we can find this probability we can use this formula:

And using the normal standard distribution table or excel and we got: