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
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
1 answer