Past records show that the times, in seconds, taken to run 100 m by children at a school can be modelled by a normal distribution with a mean of 16.12 and a standard deviation of 1.60 - Edexcel - A-Level Maths Statistics - Question 4 - 2011 - Paper 2

To find the probability, we first standardize the value using the Z-score formula:

$z = \frac{x - \mu}{\sigma}$

Where:

• $x$ = 15 (the time in seconds)
• $\mu$ = 16.12 (the mean)
• $\sigma$ = 1.60 (the standard deviation)

Calculating the Z-score:

$z = \frac{15 - 16.12}{1.60} = \frac{-1.12}{1.60} = -0.70$

Next, we look up the Z-score of -0.70 in the standard normal distribution table, or use a calculator. The table gives:

$P(Z < -0.70) \approx 0.2420$

Thus, the probability that a child runs 100 m in less than 15 s is approximately 0.242.