A random sample of 100 children is taken given that means reading age of the sample is greater that 11,65 yrs

• Sample size, $n = 100$
• Observed sample mean, $\bar{x} = 11.65$ years (assuming this is the value of interest for calculation, as in $P(\bar{X} > 11.65)$).

To calculate a z-score for the sample mean or to conduct a hypothesis test (e.g., to find the probability of observing such a sample mean), the following population parameters are needed:

• The population mean ($\mu$), which is often a hypothesized value under a null hypothesis.
• The population standard deviation ($\sigma$). If $\sigma$ is unknown, the sample standard deviation ($s$) would be needed, and a t-distribution might be used (though for $n=100$, a z-distribution is often a reasonable approximation if $s$ is used as an estimate for $\sigma$).

If the population mean ($\mu$) and population standard deviation ($\sigma$) were known, the z-score for the sample mean would be calculated as:

Once $Z$ is calculated, probabilities can be found using the standard normal distribution.

Without the population mean ($\mu$) and population standard deviation ($\sigma$), a specific numerical solution cannot be provided.