1. The problem is to determine whether each given statement about normal distribution, hypothesis testing, and probability is ALWAYS, SOMETIMES, or NEVER true. 2. Let's analyze each statement carefully: - "The parameters to be considered in normal distribution are the population mean and the standard score." The parameters of a normal distribution are the population mean ($\mu$) and the population standard deviation ($\sigma$), not the standard score (z-score). The standard score is derived from these parameters. **Answer: NEVER** - "If the graph of a normal curve is shorter and wider, the standard deviation has greater value." A larger standard deviation spreads the curve out more, making it wider and lower in height. **Answer: ALWAYS** - "If the element is 25, population mean is 25, and standard deviation is 10. The area will be equal to zero." The area under the normal curve at a single point is zero because area represents probability over an interval. **Answer: ALWAYS** - "The standard score of zero will produce an area equal to zero." A z-score of zero corresponds to the mean; the probability at a single point is zero, but cumulative area up to zero is 0.5. The statement is ambiguous but if it means area at that point, it's zero. **Answer: ALWAYS** - "The baseline of a normal curve is a number line with 6 sigma distances." The normal distribution is often shown with a range of $\pm 3\sigma$ (total 6 sigma distances) covering most data. **Answer: SOMETIMES** (commonly used but not a strict rule) - "A hypothesis statement is a prediction or an educated guess." Hypothesis is a testable prediction. **Answer: ALWAYS** - "The alternative hypothesis should always be accepted." Alternative hypothesis is accepted only if data supports it. **Answer: NEVER** - "The null hypothesis should always be rejected." Null hypothesis is rejected only if evidence is strong. **Answer: NEVER** - "In tossing a coin, the result will always be pair and balance." Single toss can be heads or tails; no guarantee of balance. **Answer: NEVER** - "In tossing 10 coins, the result will always be pair and balance." Results vary; balance is not guaranteed. **Answer: NEVER** 3. Summary of answers: | Statement | Truth Value | |---|---| | Parameters are mean and standard score | NEVER | | Shorter and wider curve means greater SD | ALWAYS | | Area at element = mean is zero | ALWAYS | | Z-score zero area is zero | ALWAYS | | Baseline is number line with 6 sigma | SOMETIMES | | Hypothesis is prediction | ALWAYS | | Alternative hypothesis always accepted | NEVER | | Null hypothesis always rejected | NEVER | | Tossing coin always pair and balance | NEVER | | Tossing 10 coins always pair and balance | NEVER | Final answers are based on statistical definitions and probability theory.