When Carson runs the 400 meter dash, his finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 2 seconds. If Carson were to run 16 practice trials of the 400 meter dash, how many of those trials would be between 73 and 75 seconds, to the nearest whole number?

Answer 1

First, we need to calculate the z-scores for 73 seconds and 75 seconds:

For 73 seconds:
z = (73 - 76) / 2 = -1.5

For 75 seconds:
z = (75 - 76) / 2 = -0.5

Next, we need to find the probability of Carson finishing the race between 73 and 75 seconds. This can be done by finding the area under the normal distribution curve between the z-scores of -1.5 and -0.5.

Using a standard normal distribution table or a calculator, we find:
P(-1.5 < Z < -0.5) = 0.6915 - 0.3085 = 0.383

Therefore, approximately 38.3% of Carson's 16 practice trials would have finishing times between 73 and 75 seconds. To find how many trials this represents, we multiply 16 by 0.383:

16 * 0.383 = 6.128

Rounded to the nearest whole number, Carson would have approximately 6 trials between 73 and 75 seconds.