A quality control manager at a factory wants to estimate the average length of bolts produced by a new machine. The standard deviation (\( \sigma \)) of the bolt lengths is known to be 0.1 mm. She takes a random sample of 50 bolts (\( n = 50 \)) and finds the sample mean (\( \overline{x} \)) is 50.5 mm. Using the formula below, where \( z = 1.96 \) is the z-score corresponding to the 95% confidence level, compute the 95% confidence interval for the true mean bolt length. Formula: \(\text{Confidence Interval} = \bar{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right)\)

Given two events \( A \) and \( B \) in a sample space \( S \), where:

Which statement best describes the law of large numbers in probability?

Antonio is a basketball player on his college team. Over the past 10 games, Antonio has scored the following number of points: 22, 18, 25, 17, 20, 25, 18, 25, 19, and 20. The coach wants to analyze Antonio’s performance to understand his scoring consistency. He decided to calculate the mean, median, and mode of Antonio’s points per game and interpret the results to inform future strategies. The data can be represented in a table as follows:     1. Based on the data provided, what is the mean number of points Antonio scored per game over the 10 games? {#1} 2. What is the median number of points Antonio scored in these games? When arranged in ascending order, the points are: 17, 18, 18, 19, 20, 20, 22, 25, 25, 25 {#2} 3. Which point total is the mode of Antonio’s points scored over the 10 games? Points Scored Frequency 17 1 18 2 19 1 20 2 22 1 25 3 {#3}

Given a continuous probability density function \( f(x) \) defined as: where \( x \) represents a continuous random variable measured in units. A graph of \( f(x) \) is shown below.

What is the role of Physio in ICU

In acid-base physiology, what does a primary metabolic acidosis with compensatory respiratory alkalosis indicate?

Which mode of ventilation is particularly useful in homogeneous lung disease like ARDS to prevent over-distension?

Which device/technique is used to facilitate non-invasive ventilation and can reduce the need for sedatives?

Which statement best defines a ‘weaning’ protocol from mechanical ventilation?