A physical fitness association is including the mile run in its secondary - school fitness test. the time for this event for boys in secondary is known to process a normal distribution with a mean of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in school can run the mile in less than 348 seconds

The probability that a randomly selected boy in school can run the mile in less than 348 seconds is 1.1%.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

μ of the time a group of boys run the mile in its secondary - school fitness test = 440 seconds

σ of the time a group of boys run the mile in its secondary - school fitness test = 40 seconds

2. Find the probability that a randomly selected boy in school can run the mile in less than 348 seconds.

Let's find out the z-score, this way:

z-score = (348 - 440) / 40

z-score = - 92/40 = - 2.3

Now let's find out the probability of z-score = - 2.3, using the table:

p (-2.3) = 0.0107

p (-2.3) = 0.0107 * 100

p (-2.3) = 1.1% (rounding to the next tenth)

The probability that a randomly selected boy in school can run the mile in less than 348 seconds is 1.1%.

0.0107

Step-by-step explanation:

z = (348 - 440) / 40 = - 2.3

1 - 0.9893

= 0.0107