Statistics help!

Question

Tennis superstar Nadal's first serve speeds in a recent season can be modeled by a normal distribution with mean 115 mph and standard deviation 6mph. let x = the speed (in mph) of a randomly selected Nadal first serve from that season. use the 68-95-99.7 rule to find:

1. probability that the serve was faster than 121 mph
2. p(109 less than or equal to 133)

thank you so much!

Answer 1

1. 121 is one standard deviation (6) above 115, so would look for percentage under curve that is greater than 1 standard deviations above mean. From Empirical Rule that would be 13.5% + 2.4% = 15.9% or 0.159 probability.
2. 109 is 1 standard deviation (6) below the mean and 133 is 3 standard deviations (18) above the mean, so would look for percentage under curve that is between 1 standard deviation below the mean and 3 standard deviations above the mean: 34% + 34% + 13.5% + 2.4% = 83.9% or 0.839 probability.