An automatic machine in a manufacturing process is operating properly if the lengths of an important sub component are normally distributed with mean =117 cm and standard deviation =5.2 cm.

a. Find the probability that one selected sub component is longer than 120 cm.

b. Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm.

c. Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.