Chapter 06, Section 6.2, Intelligent Tutoring Problem 023
Compute probabilities.
Recall the following definitions from section 6.4 of the text.
The area under the normal curve from x = a to x = b with given mean and standard deviation is the probability that x assumes a value between x = a and x = b. If we are using Table IV in Appendix C, we need to standardize the random variable x using the formula z = (x − µ)/σ, before using the table.
Alternatively, you may use a graphing calculator to obtain more accurate calculations without standardizing the random variable x.
For example, using a TI83 plus we calculate the area under the normal curve from x = a to x = b by using the
normalcdf(a,b,µ,σ)
where µ is the mean and σ is the standard deviation of the normal distribution. We use 1E99 for ∞ and−1E99 for −∞, if needed.
The 5 ages of the population have one mean. However, when looking at the 10 samples of 3 of those means, there are 10 means – one for each sample. State the symbols for the one mean and then the 10 means.