A physical fitness association is including the mile run in its secondary-school fitness test. The
time for this event for boys in secondary school is known to possess a normal distribution with a
mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 335 seconds.
) A physical fitness association is including the mile run in its secondary-school fitness test. The
time for this event for boys in secondary school is known to possess a normal distribution with a
mean of 450 seconds and a standard deviation of 60 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 312 seconds.
The mean is 450 seconds and the standard deviation is 50 seconds.
Number of standard deviations below mean
=(450-335)/50 = 2.3
Since it is assumed to be normally distributed, look up the normal distribution table to get the probability of 2.3 standard deviations lower than the mean. (approx. 1%)
anon is correct
To find the probability that a randomly selected boy in secondary school can run the mile in less than 335 seconds, we need to use the normal distribution.
Step 1: Standardize the value
First, we need to standardize the value of 335 seconds using the formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
In this case, x = 335 seconds, μ = 450 seconds, and σ = 50 seconds.
So, z = (335 - 450) / 50 = -2.3.
Step 2: Find the probability
Next, we need to find the probability associated with the standardized value using a standard normal distribution table (also known as the Z-table).
The Z-table gives us the area under the standard normal curve for different z-values.
Looking up the z-value of -2.3 in the Z-table, we find that the area to the left of -2.3 is approximately 0.0107.
Step 3: Calculate the probability
Since we are interested in the probability of the mile run being less than 335 seconds (to the left of the given value), we can subtract the area from 0.5 (which represents the total area under the curve) to get the probability.
P(X < 335) = 0.5 - 0.0107 ≈ 0.4893.
Therefore, the probability that a randomly selected boy in secondary school can run the mile in less than 335 seconds is approximately 0.4893.