8. The finishing times for a long-distance race are normally distributed, with an average finishing time of 3.25 hours and a standard deviation of 0.5 hours. If bob is running this race, what time does he need to finish in order to beat 75% of the other participants?
Step 1: You first have to write down the variables that is mentioned in the problem.
Standard Deviation: 0.5
Step 2: Since you are trying to find how much time is needed to beat 75% of the other participants, you have to find the right side of the graph rather then the left side, which makes it so you have to find the closest Z-score in the Standard Normal Distribution chart for 25% because he needs to be on the other 25% to beat the other 75%, which makes it so you have to find 0.25 in the chart.
Step 3: After finding the Z-score, you can plug in the numbers by using the formula to convert Z to X by doing x = µ + z(σ) which then turns out to be X = 3.25 + -0.67(0.5)
X = 3.25 + -.335
X = 2.915
Step 4: The number you turn out with is X = 2.915, which means that the amount of time Bob needs to finish the race beating 75% of the people is 2.915.