Question

When Jonathan runs the 400 meter dash, his finishing times are normally distributed with a mean of 88 seconds and a standard deviation of 2.5 seconds. If Jonathan were to run 48 practice trials of the 400 meter dash, how many of those trials would be between 89 and 91 seconds, to the nearest whole number?

Answer 1

To find the number of trials between 89 and 91 seconds, we need to calculate the z-scores for those values and use the z-score formula.

Step-by-step explanation:

To find the number of trials between 89 and 91 seconds, we need to calculate the z-scores for those values and use the z-score formula. The z-score formula is given by: z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. To find the z-scores for 89 and 91 seconds, we use the formula: z_89 = (89 - 88) / 2.5 and z_91 = (91 - 88) / 2.5.

Next, we use a z-score table or a calculator to find the probabilities associated with these z-scores. The probability between the two z-scores is equal to the difference between the probabilities of each z-score individually. Finally, we multiply this probability by the total number of trials to find the number of trials between 89 and 91 seconds.