Members of the track team record their times running one lap around the track. The average lap time is 105 seconds with a standard deviation of 12 seconds. Only members that rank in the top 20% will promoted to race in the next.
event. What is the time to beat so that an athlete can participate in the next event? (Remember, a lower time is best)
(a)93 seconds
(b) 95 seconds
(c) 115 seconds
(d) 117 seconds 5
To find the time to beat, we need to find the lap time that corresponds to the top 20% of the distribution.
To do this, we need to find the z-score that corresponds to the top 20% of the distribution. The area to the left of the z-score will be 1 - 0.20 = 0.80.
Using a standard normal distribution table or a calculator, we find that the z-score corresponding to an area of 0.80 is approximately 0.84.
Next, we can use the formula for z-score to convert the z-score back to a lap time:
z = (x - μ) / σ
0.84 = (x - 105) / 12
Multiplying both sides by 12, we get:
10.08 = x - 105
Adding 105 to both sides, we get:
x = 115.08
Therefore, the time to beat for an athlete to participate in the next event is approximately 115 seconds.
(c) 115 seconds