Question

part 2 - calculation questions. please provide your final answer in the box. points are awarded for correct answers - partial marks will not be provided. (6 marks)

1. you measured the length of three cheek cells (x_{1 - 3}) in \\( \mu m \\):

\\( x _ { 1 } = 15.2 \mu m \\)
\\( x _ { 2 } = 16.5 \mu m \\)
\\( x _ { 3 } = 17.8 \mu m \\)
calculate the mean and sem for the length of your cheek cells. report your final value to one decimal place. show all your work for both calculations. (2 marks)
mean
\\( \overline { x } = \frac { \sum x _ { i } } { n } \\)
sem
\\( \mathrm { sem } = \sqrt { \frac { \sum ( x - x ) ^ { 2 } } { n ( n - 1 ) } } \\)
mean =
sem =

1. the image below shows a serial dilution of a stock solution of 100 mg/ml enzyme. what is the concentration of enzyme in tube #5? round your answer to two decimal places and include units. (1 mark).

concentration in tube #5 =

Explanation:

Question 1

Step1: Calculate sum of lengths

$\sum x_i = 15.2 + 16.5 + 17.8 = 49.5$

Step2: Compute mean

$\bar{x} = \frac{\sum x_i}{n} = \frac{49.5}{3} = 16.5$

Step3: Calculate squared deviations

$(15.2-16.5)^2 + (16.5-16.5)^2 + (17.8-16.5)^2 = (-1.3)^2 + 0^2 + 1.3^2 = 1.69 + 0 + 1.69 = 3.38$

Step4: Compute SEM

$SEM = \sqrt{\frac{3.38}{3-1}} = \sqrt{\frac{3.38}{2}} = \sqrt{1.69} = 1.3$

Step1: Determine dilution factor per step

Each step: 50 μL enzyme + 450 μL buffer → total volume = 500 μL. Dilution factor per step: $\frac{50}{500} = 0.1$

Step2: Total dilution factor for Tube #5

5 steps: $(0.1)^5 = 10^{-5}$

Step3: Calculate concentration

Concentration = $100 \times 10^{-5} = 0.001$ mg/mL (rounded to two decimal places: 0.00 mg/mL)

Answer:

Mean = 16.5 μm
SEM = 1.3 μm

Question 2